MGWS                                                                                                                                                                                                          (                                                                                                                                                                                                                                                                                                                                                                                                          l                                $      (      ,      0      4      8      <      @      D      H      L      P      T      X      \      `      d      h      l      p      t      x      |                                                                                                                     <  H  D      P          H      X  l  p  t              $     (                                                                                                                                                                                                                                                                                                                                 $                                                                                   t         |         `;                   4                                                                                                                                                   `                                      @                                          8                                                                                                                                                                                                                                                                                                                                   $    #  01 4F    d                                                                                                                           w  t    P     T  d  h                 x       
   D     ?     T     ?     tn     ?     \     d  "   ,$  T   8h     p\     A     (     dF     dF     \     \     ,          x          *     *     *     *                       (         E    \    \  "  8.  +    ,    1  TS  4  3  :    ;  @-  ?  n  B  E  F  8u  H  S  J  p  K  (  a  _  ~      <W    |~    q    E    L    +        d        Hm    l    E            P>    0>    O            4^    lN       "  T  4  m  7  m  N  '  R  h  _    |  ,        N    N    m    4    ]    
    '    ^        pI    H.              ,  X@  /  Y  0    7  H  =    X  <U  i  4  t  @=    xH    .    h9    .    H    H    \+        `Q    X        o    8    h    Y    PH    1    tk    L+    L+        ܉    ,    x    |b    n    E  &  E  0  o  ?  (.  A  ;  K  (  M  l  [  $  `  (  a    i  (    R    +    \C                HM    (N    '    (-        HM        4V     \  4  n  9  to  =  *  ?  *  G    N  p>    >                xV    _             5  
  `K    0    h  1  	  3  8  F    G    Z  C  i     j    k  S  q  0  u  P(  w  @(        D    <    <        '                  u  !  )  .     /  +  4     5  +  8  @  c    s  l  |  te        2            0/        D    $7    q    LW    $+    pO     d    u    =      &    *    1  (  R    X     \                  `         d            
            d      #     ȶ  A(  
      	   __sig__29   D    B(            |                  C(        -   Returns all quaternion ideals isogenous to A.   
  D(                                                                       |      E(  
      	   __sig__30       F(            |                  G(  
         IsogenousIdeals t  H(                                               I(  2         Returns the left ideal of A generated by p^n and (a + b*x1)*x2^n, where Q = <a,b> with GCD(a,b) = 1. Here (q = p^n, x2^n) is the nth power of a split prime (p,x2) in Z[x2].       J(                                                           0  |  $  #  K(  
      	   __sig__31   $  $  L(            |  ,              &  M(  
         IsogenousIdeal  '  N(                 (                              O(        M   Returns the level of a positive definite quadratic form having Gram matrix M.   /  P(                                                                     H  |  <  2  Q(  
      	   __sig__32   P4  h4  R(            |  D              5  S(  
      	   FormLevel   7  t8  T(                 @                              U(        @   Returns the number of classes in the Brandt groupoid of level N. <  <  <  V(                                                                 p  `  |  T  @  W(  
      	   __sig__33   HB  B  X(            |  \              D  v(                                                                       ԡ    y(  
         CompareForms 	  p	  z(                 ء                              {(        2   Returns the InnerProduct(x*M,y) with respect to M.  L  d  |(                         9    9                                           }(  
         __sig__5       ~(                              (        V   Returns the matrix N such that M*N = N*M is the determinant times the identity matrix.     (                                                                              (  
         __sig__6 !  "  "  (                            |#  Y(           LevelClassNumber H  H  I  Z(                 X                              [(        D   Returns the number of classes in the Brandt groupoid of level (N,M). P  PP  \(                                                                   x  |  l  T  ](  
      	   __sig__34   \U  U  ^(            |  t              W  _(        *   /home/was/magma/Kohel/quadratic_modules.mg  $`(        *   /home/was/magma/Kohel/quadratic_modules.mg  $a(        Y   Returns the unique Minkowski reduced representative for QF, and the transforming matrix.    a  a  b(                                                                           8g  c(  
         __sig__0 h  h  i  d(                            j  e(           MinkowskiReduction  l  l  f(                                               g(         `   Returns the matrix obtained by a basis permutation such that QF[i,i] le QF[j,j] for all i le j.  w  w  w  h(                                                                           z  i(  
         __sig__1 {  {  {  j(                            <}  (           ClassicalAdjoint        (                                                (        ]   Returns the determinant of the matrix obtained by removing the ith row and jth column from M.     (                                                                         (  
         __sig__7       (                            t  (           MinorDeterminant       (                                               (        /   Returns 1 if x and y are equal and 0 otherwise.   0  H  (                                                                    8    ,  !  (  
         __sig__8 "  "  "  (              4              $  k(  
         NormEchelon ~  ~  l(                                               m(  ,         Returns true if and only if QF[i,i] le QF[j,j] and 2*|QF[i,j]| le M[i,i] for all i le j. This is weaker than the matrix being Minkowski reduced.       8  n(                                                                           `  o(  
         __sig__2     $  p(                              q(  >         Compare two matrices under the ordering obtained by defining as smaller the matrix with the smallest first diagonal element, or, in absolute value, the largest off-diagonal element, under an ordering of the entries.    $  \  r(                                                                   С    ġ  8  s(  
         __sig__3       t(              ̡                u(        W   Return 1 if M1 is less than M2, 0 if M1 and M2 are equal, and -1 if M2 is less than M1. X  p    w(  
         __sig__4       x(              ܡ              L  d    (  
         KroneckerDelta     (                 0                              (        %   /home/was/magma/Kohel/power_series.mg XU   r     _             d5                  d5                  d5                  d5                  d5                  d5                  d5                  d5                  H6                   d5       $           d5       (           d5       ,           d5       \           d5       |           d5                  d5                  d5                  d5                  d5                  d5                  	d5                  d5                  d5                  d5                   d5       $           d5       (           d5       ,            d5       0           $d5       4           'd5       8           5       h           7z2                  5                  o6                   o6       	           o6       	           	o6        
           *t6       x
           SQ7       
           E^3       0           ~z2                  z2                  Zz2                  yz2                  63       8           Tz2       p           bz2                  Bz2                  lz2       H           pz2       h           uz2                  gz2                  =z2                  Pz2                  If3       0           1f3       H           -Z6                  #3       0           Ef3       P           '7                  <R'4                  4                  6                  p*1                  9'w7       4           d3       l           &5                  8{1                  1                  6       D           ow5                  <X5                  Em3                  /Q3       $           u2       T           h7                  5       |           [7                  >2                  u6                  1                  
*1       d           z1                  7       @           7       %           ~92       %           t6       &           {4       '           vl2       $'           2       d'           RH3       '           5       '           jZ6       ,(           Ҏ5       \(           Gx7       (           >5?3       (            3       (           W3       )           d5       L*           4       P*           4       *           4       h+           Kӽ5       +           14       +           84       +           *4       ,           Խ5       @,           )c6       `,           ;4       ,           4       4-           j7       /           7       T1           0R7       X1           L7       1           7       2           i7       <3           7       3           7        4           7       p4           ڇx6       4           7       4           t6       05           d5       p6           d5       7           +7       7           +7       7           +7       7           7       7           +7       7           +7       7           +7       7           +7       7           S7       7           7       ;           7       4=           d5       =           -{7       >         >  a7       >         >  a7       >         >  a7       ,?         >  a7       0?         >  a7       4?         >  a7       8?         >  a7       <?         >  a7       @?         >  a7       `?         >  a7       ?         >  a7       ?         >  a7       ?         >  a7       ?           (5       ?           oX5       ?           a(5       ?           [t6       L@           t6       @         @  7       XA         @  7       A         @  7       B         @  7       C         @  7       E         @  7       E         @  7       I         @  7       lJ         @  7       <K         @  7       K         @  7       K         @  7       L         @  7       M         @  7       N         @  7       LO         @  7       P         @  7       P         @  7       lQ         @  7       ,R         @  7       R         @  7       HS         @  7       (T         @  7       @V         @  7       V         @  7       V         @  7       W         @  7       W         @  7       TX         @  7       X         @  7       `Y         @  7       Y         @  7       d[         @  7       [         @  7       [         @  7       \         @  7       4\         @  7       ]         @  7       ^         @  7       |_         @  7        a         @  7       Xa         @  7        b         @  7       b         @  7       b         @  7       c         @  7       Pd         @  7       d         @  7       le         @  7       e         @  7       xf         @  7       f         @  7       g         @  7       h         @  7       i         @  7        k         @  7       k         @  7       m         @  7       o         @  7       p         @  7       Xq           7       4s  4    0s  v8                 0s  #g8        ܒ         0s  7        ,         0s  7        D         0s  i7                 0s  i7        Ȕ      0s  |7        Ė         0s  Hk7                 0s  i7        `         0s  k7                  0s  nl7                 0s  nl7                 0s  nl7        x         0s  j7        |         0s  k7        D         0s  k7        |         0s  Hk7                                                                (        %   /home/was/magma/Kohel/power_series.mg (        I   Returns the echelonized sequence of power series spanning the same space. 0(                                                                   X  H  L  (  
         __sig__0 P(            H  T              0(  
         EchelonSeries X(                 P                              (        ;   Returns the echelonized basis for the space generated by B. X(                                                                   p  H  d  (  
         __sig__1  p(            H  l              (            /usr/local/magma-2.5/libs                    J   examples:galpols:glnzgps:intro:isolgps:matgps:perfgps:pergps:simgps:solgps                      /tmp                     
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block system of M                                 z                                            $             
         __sig__1                                                 
         __sig__8  ters               F   Return prime and exponent of the extraspecial subgroup normalised by M                                j                                        D  4    (         
         __sig__2                           0                              ExtraSpecialParameters                        ,                                       F   Return prime and exponent of the extraspecial subgroup normalised by M                                z                                            L    @         
         __sig__3                           H                           %   Return the extraspecial subgroup of M                                 j                                 j       d  \    P         
         __sig__4                           X                           %   Return the extraspecial subgroup of M                                 z                                 j           l    `         
         __sig__5                           h                              The tensor factors of M                                       z                                          |    p         
         __sig__6                           x                     
         TensorFactors                         t                                          The tensor factors of G                                       j                                                         
         __sig__7                                                      N   Return the change of basis matrix which exhibits the tensor decomposition of M                                z                                                                                       
         AreProportional     
         __sig__1   T       
         TensorBasis                                                                  N   Return the change of basis matrix which exhibits the tensor decomposition of G                                j                                                         
         __sig__9                                                
      	   __sig__12 sion               &   The degree of the field extension of M                                z                                                                                        
      	   __sig__10                       DegreeOfFieldExtension      (     D                                                           &   The degree of the field extension of G                                j                                                         
      	   __sig__11                                                        The centralising matrix of M                                  z                                                                                                SymmetricTensorFactors  $              CentralisingMatrix                                                                      The centralising matrix of G                                 j                                                         
      	   __sig__13                                           .  
      	   __sig__22 mutations             The Frobenius automorphisms of M                                     z                                        ,              
      	   __sig__14                                                      FrobeniusAutomorphisms      	                                               
            The Frobenius automorphisms of G                                     j                                            4    (        
      	   __sig__15                         0                          #   Return the symmetric tensor factors                                  z                                          D    8        
      	   __sig__16                         @                             SymmetricTensorPermutations L  d                   <                                      !   Return the symmetric tensor basis                                    z                                          \    P        
      	   __sig__17                         X                             SymmetricTensorBasis                         T                                      E   Return the permutations of the factors induced by the generators of M                                z                                          t    h        
      	   __sig__18                         p                  R                 8                                               l                                       #   Return the symmetric tensor factors         !                         j                                                      "  
      	   __sig__19           #                                $        !   Return the symmetric tensor basis           %                         j                                                      &  
      	   __sig__20           '                                (        E   Return the permutations of the factors induced by the generators of M       )                         j                                                      *  
      	   __sig__21           +                                ,            The block permutation group of G            -                         j                                                    /                                0            The block permutation group of M            1                         z                                                      2  
      	   __sig__23           3                                4        8   /usr/local/magma-2.5/package/GrpMat/Smash/is-primitive.m    TP{E        5   /usr/local/magma-2.5/package/GrpMat/Smash/minblocks.m UF        2   /usr/local/magma-2.5/package/GrpMat/Smash/minsub.m .pUUU  
         __sig__1            6        3   Attempt to decompose G wrt normal closure in G of E         7                             j                                                8  
         __sig__0            9                                :           SearchForDecomposition      ;                                               =                         j                                                    >  
         __sig__1            ?                                @           True iff M is primitive             A                         z                                                     B  
         __sig__2            C                                D        .   /usr/local/magma-2.5/package/GrpMat/Smash/is.m P{H        3   /usr/local/magma-2.5/package/GrpMat/Smash/numbers.m hYZI        6   /usr/local/magma-2.5/package/GrpMat/Smash/order-test.m ZJ        2   /usr/local/magma-2.5/package/GrpMat/Smash/random.m tZZO  
         __sig__0            G        0   /usr/local/magma-2.5/package/GrpMat/Smash/misc.m m  ZP{L        6   /usr/local/magma-2.5/package/GrpMat/Smash/semilinear.m `\M           True iff G is semilinear         N                         j                                        P  @  0  4      P            0  <                  
         GroupGenerators              q   H     Q  
         IsSemiLinear        K        6   /usr/local/magma-2.5/package/GrpMat/Smash/semilinear.m P{        1   /usr/local/magma-2.5/package/GrpMat/Smash/smash.m   \h^        4   True iff G is known to be a symmetric tensor product                                j                                                  H6  
         __sig__0       $                                             IsSymmetricTensor          
         __sig__0            S           True iff M is semilinear            T                         z                                            X  0  L      V            0  T                  W        6   /usr/local/magma-2.5/package/GrpMat/Smash/smash-spec.m P{X        6   /usr/local/magma-2.5/package/GrpMat/Smash/smash-spec.m P{[  
         BlockNumbers        \  
      
   BlockSizes          ]  
         NmrOfBlocks         i           DegreeOfFieldExtension  !   f           ExtraSpecialGroup        g           ExtraSpecialParameters  0  j  
      
   LinearPart        }  
         __sig__2    (   )   h           SemiLinearFlag           a           TensorProductFlag           e           ExtraSpecialFlag        !   "   #   m           SymmetricTensorProductFlag       s        3    Return G-module generated by sequence of matrices  (   )   o           SymmetricTensorPermutations    H             qq                   q3d $   %           
   randomSeed  .   /   0   1   p           SymmetricTensorBasis        l           FrobeniusAutomorphisms  !   y  
         __sig__1 em *   +   k           CentralisingMatrix          n           SymmetricTensorFactors  !   u           __sig__0 s nsorBasis s  !              squareDiscriminat       !              signum  )              sl  0   1              so  8   9     
         identity      8             field   H             su                   sp  $   %     
      	   recognize   .   /              forms   7           
   generators              q                              !   "   #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   t                                                          z           `        v            `                    w        .    Return G-module generated by set of matrices       x                                                          z             `        z            `                    {            Return degree of matrix g          |                         k                                             `        ~            `                                 Return degree of matrices of G                                      j                                        dU    `          
         __sig__3                        `                               p pMat  ld          &    Return the dimension and field for G                                j                                         (    `          
         __sig__4                        `                      
         BasicParameters                                                            &    Return the dimension and field for G                                                                         8  0  `  $        
         __sig__5                        `  ,                          3    Return the dimension and field for the G-module M                                   z                                             @  `  4        
         __sig__6                        `  <                          C    Return a sequence containing generators of the underlying group G                                                                           `  P  `  D        
         __sig__7                        `  L                                                                                  H                                      C    Return a sequence containing generators of the underlying group G                                   z                                        p  h  `  \        
         __sig__8                        `  d                          8    Return a sequence containing generators of the group G                                      j                                            x  `  l        
         __sig__9                        `  t                          1   /usr/local/magma-2.5/package/GrpMat/Smash/smash.m   qP{        2   /usr/local/magma-2.5/package/GrpMat/Smash/tensor.m rhqHs        3   /usr/local/magma-2.5/package/GrpMat/Tensor/action.m qHs        3   /usr/local/magma-2.5/package/GrpMat/Tensor/direct.m rHs        ;   /usr/local/magma-2.5/package/GrpMat/Tensor/factorise-poly.m XrHs        7   /usr/local/magma-2.5/package/GrpMat/Tensor/find-point.m Hs                            Mat/                                                       ;   /usr/local/magma-2.5/package/GrpMat/Smash/stabiliser-test.m sP{        6   /usr/local/magma-2.5/package/GrpMat/Tensor/is-tensor.m `v        <   /usr/local/magma-2.5/package/GrpMat/Tensor/is-projectivity.m t`v        6   /usr/local/magma-2.5/package/GrpMat/Tensor/is-tensor.m `v           True iff G is a tensor product  $                           j                                                      
         __sig__0                                                           t                                         k     T             IsTensor                            7   /usr/local/magma-2.5/package/GrpMat/Tensor/find-point.m       4         Decide whether or not the collection of matrices X is composed of k x k blocks which differ only by scalars; if so, return true and the decomposition of each matrix, else false                                                                                           
         SemiLinearGroup              d mallerFiel                                                 ,         Decide whether or not the matrix X is composed of k x k blocks which differ only by scalars; if so, return true and the decomposition, else false                                                                                                                          
         IsProportional                                                             5   /usr/local/magma-2.5/package/GrpMat/Tensor/groebner.m P{        2   /usr/local/magma-2.5/package/GrpMat/Tensor/local.m  zh}        2   /usr/local/magma-2.5/package/GrpMat/Tensor/order.m 5zh}                                  
         __sig__0                       l  x                          2   /usr/local/magma-2.5/package/GrpMat/Tensor/pdash.m  8{h}        3   /usr/local/magma-2.5/package/GrpMat/Tensor/plocal.m {h}        7   /usr/local/magma-2.5/package/GrpMat/Tensor/stabiliser.m h}        (   /usr/local/magma-2.5/package/GrpAb/hom.m ppd(|x|ʸ        ?   /usr/local/magma-2.5/package/GrpMat/SmallerField/SmallerField.m h}        ?   /usr/local/magma-2.5/package/GrpMat/SmallerField/SmallerField.m h}           True iff M is a tensor product                               z                                                        
         __sig__1                    3   /usr/local/magma-2.5/package/GrpMat/Tensor/jordan.m `~P        2   /usr/local/magma-2.5/package/GrpMat/Misc/semilin.m  ~H        1   The semilinear extension of G over the subfield S d5                                q    j                           j           |  l  p  H6  
         __sig__0       $  /  
         IsLinearGroup     0                                                       #           RecognizeClassical  H  `  '           __sig__1     P              2   /usr/local/magma-2.5/package/GrpMat/Misc/rewrite.m  H        2   /usr/local/magma-2.5/package/GrpMat/Misc/rewrite.m 50H                         q    j                           j                  $d5  
         __sig__0       8                                            "      k   Does G have an equivalent representation over a subfield? If so, return true and equivalent representation.                                  j                                  j       \  L  <  @                 IsOverSmallerField                           D                                &      w   Does G have an equivalent representation over a subfield of degree d? If so, return true and equivalent representation.                                          j                            j           d  <  X        
         __sig__1                        <  `                          2   /usr/local/magma-2.5/package/GrpMat/Misc/semilin.m   P           Entropy und   "      j   Use the Niemeyer-Praeger algorithm to test whether <grp> contains the corresponding classical group Omega.                                  j                                              x  |     !  
         __sig__0          "            x                ,  1        L   Return true if grp is known to be contained in GSp(d,q) and contains Sp(d,q)         $                                               %  $      r   Return the type if <grp> is known to be a classical matrix group in its natural representation and false otherwise       &                         j                                              x        (            x                   )  
         ClassicalType      *                                               -  
         __sig__2             <         Given a group G of d by d matrices over a finite field E having degree e and a subfield F of E having degree f, write the matrices of G as d*e/f by d*e/f matrices over F and return the group and the isomorphism                     WriteOverSmallerField                                                              =   /usr/local/magma-2.5/package/GrpMat/ClassicalRec/attributes.m P        <   /usr/local/magma-2.5/package/GrpMat/ClassicalRec/classical.m  P  
      
   containsSL                    isSL    '              isGL    /     
      
   primeField  8   9     
      	   statistic   B   C     
         randomProcess   L    
         isCRecSL            
         smallRandom (   )              ranges  1     
         dualGenerators  ;   	           abstractIdentity    F   G   H   I     
      
   printLevel                  matmap       
         orderSL %   &   '     
         transvection    1              transvectionBasis   <   =              useTransvection G   H   I              ext P   Q              moreAbstractGens          
         abstractGroup                spanningConjugatingElements "   #              spanningBasisInverse    /     
         spanningBasis   9     
         rewritingRules  C     
      	   detOrders   L   M              order   U     
         abstractSeed   
         almostElement                root                 rootDeterminant                   images            <   /usr/local/magma-2.5/package/GrpMat/ClassicalRec/classical.m 
           abstractGenerators                                   j                                                 /                               ;              NumberOfInvariantForms  G                                                    
         __sig__1    _   `   +        K   Return true if grp is known to be contained in GL(d,q) and contains SL(d,q)      ,                         j                                              x      .            x                   I  
         ClassicalForms    J                 	                              ;           IsOrthogonalGroup   H  `  <                                               2                         j                                              x    C   3  
         __sig__3    L   M   4            x                X   Y   Z                            j                                          P    D      
         __sig__2 	  X	  p	                L              
             NumberOfAntisymmetricForms  \  t                   H                                       e   The symmetric and anti-symmetric invariant forms of G (the first symmetric form is positive definite)   (          (   /usr/local/magma-2.5/package/Lat/genus.m           2   The genus of L (the non-isometric neighbours of L)                                                                        Y        <    
         __sig__0      P                              h             Sforms      D        8   /usr/local/magma-2.5/package/GrpMat/ClassicalRec/forms.m   E        D   returns record storing the classical forms of the matrix group <grp> d5    F                         j                                            	  	  	    G  
         __sig__0 d5       H            	  	              d5a           ScalarsSymmetricBilinearForm   `  b                 x	                              U           ScalarsSymplecticForm   `  V                 H	                              L                         j                                            8	  	  ,	  (  N            	  4	                  O  
         SymplecticForm      P                 0	                              _  
         __sig__4 Form      (           M148 alentin
           x   5           IsSymplecticGroup           9  
         __sig__4            (  
         eps Determinant; ; oQ        8   If <grp> preserves a symplectic form, return the scalars                    6                                               7  $      t   Returns true if grp is known to be contained in GO^e(d,q) and contains the corresponding subgroup Omega of SO^e(d,q)        8                         j                                              x        :            x                    K        5   If <grp> preserves a symplectic form, return the form     M           __sig__1         	  =        H   Return true if grp is known to be contained GU(d,q) and contains SU(d,q)            >                         j                                             	  x        ?  
         __sig__5            @            x                    A  
         IsUnitaryGroup      B                                               C        8   /usr/local/magma-2.5/package/GrpMat/ClassicalRec/forms.m    ؟P  :         An abelian group A isomorphic to Hom(G, H) (where G and H are finite abelian groups), together with the transfer map t which, given an element of A, returns the corresponding group homomorphism from G to H                                                                     
  
  
  
        
         __sig__0      d5            
  
                   <         An abelian group A isomorphic to Hom(G, H) (where G and H are finite abelian PC groups), together with the transfer map t which, given an element of A, returns the corresponding group homomorphism from G to H d5                                                                          $
  
  
  d5  
         __sig__1       0              
   
                    (         A sequence of (Z-module) generators of the set of all homomorphims from the finite abelian group G to the finite abelian group H           
         __sig__2            R                         j                                            P	  	  D	      S  
         __sig__2            T            	  L	                  c        4   If <grp> preserves a quadratic form, return the form     f            	  	              	  W        =   If <grp> preserves a symmetric bilinear form, return the form       X                         j                                            h	  	  \	      Y  
         __sig__3            Z            	  d	                  [           SymmetricBilinearForm       \                 `	                              e           __sig__5 ilinearForm        ]        ?   If <grp> preserves a symmetric biliner form, return the scalars             ^                         j                                            	  	  t	      `            	  |	                  }  
         FormType       ~                 	                                                          e/bkab.m m  q           ScalarsUnitaryForm  H  `  r                 	                                         Modules r s d                         j                                            	  	  	      o  
         __sig__7 orm        g        7   If <grp> preserves a quadratic form, return the scalars             h                         j                                            	  	  	      i  
         __sig__6            j            	  	                  k           ScalarsQuadraticForm        l                 	                              m        5   If <grp> preserves a unitary form, return the scalars       n                         j                                            	  	  	      p            	  	                          6   /usr/local/magma-2.5/package/GrpMat/ClassicalRec/ppd.m 8        (   /usr/local/magma-2.5/package/GrpAb/hom.m ica8ʸs        2   If <grp> preserves a unitary form, return the form          t                         j                                            	  	  	      u  
         __sig__8            v            	  	                  w  
         UnitaryForm         x                 	                              y        4   If <grp> preserves a classical form, return its type        z                         j                                            	  	  	      {  
         __sig__9            |            	  	                    
         SrivastavaCode                     
                                          |
  
              	             AllHomomorphisms   H  `                   T
                                         __sig__5 	  	  	  	  8
          (   /usr/local/magma-2.5/package/Code/cons.m   p  
         __sig__1 tavaCode     b      h  Given sequences alpha = [a_1, ..., a_n], W = [w_1, ..., w_s], and Z = [z_1, ... z_k] of elements from the extension field K of the finite field S, such that the elements of alpha and Z are non-zero and the n + s elements of alpha and W are distinct, together with an integer t > 0, construct the generalized Srivastava code of parameters alpha, W, Z, t, over S                                   q       r   r   r         H           
  |
  
       
         __sig__0                      |
  
                            GeneralizedSrivastavaCode      (                   
                                                       q       r   r               H           
  |
  
                |
  
                    
         GabidulinCode                        
                                         __sig__3                                                                                   D
  4
  
  (
                  
  0
                    
         HomGenerators                        ,
                                (         A sequence of (Z-module) generators of the set of all homomorphims from the finite abelian PC group G to the finite abelian PC group H                                                                         L
  
  @
        
         __sig__3                        
  H
                          \   A sequence of all homomorphims from the finite abelian group G to the finite abelian group H                                                                       l
  \
  
  P
        
         __sig__4                        
  X
                                              r   r   r               H           
  |
  
      
         __sig__2 	  X	  p	  6           Primes  
           b   A sequence of all homomorphims from the finite abelian PC group G to the finite abelian PC group H                                                                             t
  
  h
                  
  p
                          (   /usr/local/magma-2.5/package/Code/cons.m    кP        (   /usr/local/magma-2.5/package/Code/iaks.m     
         __sig__1 ation        &      x   Generate the homomorphic image of Code in a SubField, i.e., each symbol in Code is represented as sequence over SubField      H6                         q    H                           H           
  
  
       
         __sig__0   d5                
  
                           SubfieldRepresentation                       
                                      <   Construct the concatenated code from OuterCode and InnerCode   d5                         H    H                           H             
                    
                0                               q                           H           \  4  P      
         __sig__1 	  X	  p	              4  X              
    ,                               r    H                     H           $  
                  __sig__2                      V      :  Given sequences alpha = [a_1, ..., a_n] and W = [w_1, ..., w_s] of elements from the extension field K of the finite field S, such that the elements of alpha are non-zero and the n + s elements of alpha and W are distinct, together with an integer mu, construct a Srivastava code of parameters alpha, W, mu, over S                     ConcatenatedCode                                                                   
                 	             Relat   
    
         ChienChoyCode                       
                                
         MaxOrthPCheck ackage           Aforms ʸ  @         Given alpha = [a_1,...a_n], and w = [w_1,...w_s] a sequence of n+s distincts elements of GF(q), z, a sequence of n nonzero elements of GF(q), and t > 0, construct the Gabidulin MDS code of parameters alpha, w, z, t over GF(q)             Z      M  Given polynomials P and G over a finite field F, an integer n > 1, together with a subfield S of F, such that n is coprime to the cardinality of S, F is the splitting field of x^n - 1 over S, P and G are coprime to x^n - 1 and both have degree less than n, construct the Chien-Choy generalised BCH code with parameters P, G, n over S                                q                           H           
  |
  
                  |
  
                    *         Construct the Justensen code from RSCode and a primitive element alpha of the alphabet of RSCode the powers of the innercode are shifted by k   <
                                                            H                     
         SimplexCode                                                             (   /usr/local/magma-2.5/package/Code/fire.m           (   /usr/local/magma-2.5/package/Code/fire.m d5(  *         Given a polynomial h in GF(q)[X], a nonnegative integer s, constructs a Fire code of length n of generator polynomial h*(X^s - 1) over GF(q)                                                             H                 	d5  
         __sig__0                                                 L   Return the Elias asymptotic upper bound for delta in [0, 1] over the field K                              V    q                           V           <    0  d          *   /usr/local/magma-2.5/package/Code/random.m          H   Return a random linear code of length n and dimension k over the field K 
                                          q                     H                       
         ZeroCode                        <                                      '   Return the [n,n,1] universe code over F 8
  `
  
    
         JustensenCode                                                              *   /usr/local/magma-2.5/package/Code/simple.m  P     
   *   /usr/local/magma-2.5/package/Code/simple.m  PP        #   Return the [n,0,n] zero code over F                                      q                           H           D  4  8        
         __sig__0                        4  @                    
         EvenWeightCode                                                           +   /usr/local/magma-2.5/package/Code/simplex.m  p  
         __sig__0   x      
         RepetitionCode                      l                                      )   Return the [n,n-1,2] zero-sum code over F   
  
    
         UniverseCode                         T                                      #   Return the [n,1,n] zero code over F                                      q                           H           t  4  h        
         __sig__2                        4  p                          +   /usr/local/magma-2.5/package/Code/simplex.m x        0   Return the [2^r-1,r,2^(r-1)] simplex binary code 	  	  	                              ,                               q                           H             4          
         __sig__3                        4                      
         ZeroSumCode                                                                0   Return the [n,n-1,2] even-weight code over GF(2)                                                                      H             4          
         __sig__4                        4                    
  
      
   EliasBound                                                        
         __sig__4 inearBound   
         __sig__1 
  
  
                8                  
         FireCode                                                               *   /usr/local/magma-2.5/package/Code/random.m   p   
         __sig__0            .   )   /usr/local/magma-2.5/package/Code/bound.m   pp  $      v   Return the upper Elias bound for the cardinality of a largest code of length n and minimum distance d over the field K                                      q                                $      d5  
         __sig__0       ,  	                                 "           GilbertVarshamovAsymptoticBound `  #                 |                              '                            8
  (           GriesmerLengthBound x               Modi   p             GilbertVarshamovBound   `                   L                                                               q                                l    `               EliasAsymptoticBound   5                 4                                (         Return the Gilbert-Varshamov lower bound for the cardinality of a largest code of length n and minimum distance d over the field K    ~z2                                 q                                T    H                                                  RandomLinearCode                                                                   )   /usr/local/magma-2.5/package/Code/bound.m   P        +   /usr/local/magma-2.5/package/Code/entropy.m X        U   Computes the entropy function for a real number in the interval [0,1-1/q], where q=#S d5                             q    V                           V           L  <  @      
         __sig__0 d5                   <  H              d5  *         Return the best known lower bound and upper bound for the cardinality of a largest code of length n and minimum distance d over the field K 	  <
                                   q                                           
         __sig__0                   <  `              (    
         InformationRate                    \                                      )   /usr/local/magma-2.5/package/Code/ispow.m           )   /usr/local/magma-2.5/package/Code/ispow.m o6        M   Test if Q is a power of q>0, then return true and the exponent or false and 0   SQ7                                                                      t  x       
         __sig__0   yz2                t                      
         __sig__2                          P                  $  "      k   Return the Griesmer lower bound of the length of a linear code of dimension k and minimum distance d over K (	  @	  %                                 q                                      D  \  t    (         Return the Gilbert-Varshamov lower bound of the size of a largest linear code of length n and minimum distance d over the field K             
         __sig__3                          h                             GilbertVarshamovLinearBound                          d                              &           __sig__5 symptoticBound       $      p   Return the Gilbert-Varshamov asymptotic lower bound of the information rate for delta in [0, 1] over the field K                                     V    q                           V               x      !                                :  
         GriesmerBound     ;                                               <  "      n   Return the Johnson upper bound for the cardinality of a largest binary code of length n and minimum distance d  @  .  
      	   IsOptimal        /                                               8  
         __sig__8 ightBound  1                                 q                                        )                                               *        S   Return true if the linear code is optimal for the Griesmer bound, else return false         +                         H                                                      ,  
         __sig__6            -                                =                                                                           >  
         __sig__9 	  X	  p	  ?                            
  @  
         JohnsonBound                SQ roc t  t 0  $      t   Compute the Griesmer upper bound of the minimum weight of a linear code of length n and dimension k over the field K        2  
         __sig__7            3                                4           GriesmerMinimumWeightBound          5                                               6  "      m   Return the Griesmer upper bound of the cardinality of a linear code of length n and minimum distance d over K       7                                 q                                          9                                R           McElieceEtAlAsymptoticBound H  `  S                 <                              T  $      p   Return the Plotkin upper bound of the cardinality of a largest code of length n and dimension d over the field K       F  
         IsNearlyPerfect    G                                               H  (      w   Return the Levenstein upper bound of the cardinality of a largest code of length n, minimum distance d over the field K            A                                               B        C   Return true if the binary code is nearly perfect, else return false         C                         H                                                      D  
      	   __sig__10           E                                U                                 q                                \    P    W              X              	  X  
         PlotkinBound 
  
  Y                 T                              I                                 q                                ,           J  
      	   __sig__11           K              (                  L           LevenshteinBound            M                 $                              V  
      	   __sig__13 oticBound N  $      t   Return the McEliece-Rodemich-Rumsey-Welch asymptotic upper bound of the binary information rate for delta in [0, 1].        O                         V                                 V           D    8      P  
      	   __sig__12           Q              @                  j  
         SingletonBound    k                                               t  
      	   __sig__18 cBound 	  l  "      m   Return the Singleton asymptotic upper bound of the information rate for delta in [0, 1] over any finite field   0  ^  
         IsEquidistant      _                 l                              h  
      	   __sig__16 ound  	  `  "      f   Return the Plotkin asymptotic upper bound of the information rate for delta in [0, 1] over the field K  0  H  `  Z        9   Return true if the code is equidistant, else return false           [                         H                                            t    h      \  
      	   __sig__14           ]              p                  m                         V                                 V                   n  
      	   __sig__17   X	  p	  o                            
  p           SingletonAsymptoticBound   \  t  u                              a                         V    q                           V                     b  
      	   __sig__15           c                                d           PlotkinAsymptoticBound      e                                               f  $      v   Return the Singleton upper bound of the cardinality of a largest code of length n, minimum distance d over the field K      g                                 q                                          i                                           HammingAsymptoticBound                                                      &      z   Return the "Van Lint" lower bound to the size of a largest linear code of length n and minimum distance d over the field K              	   __sig__22           v  
         SphereVolume      w                                               x  (         Return the Hamming spheres packing upper bound of the cardinality of a largest codes of length n and dimension d over the field K                   Nends  k m  q                                               r        J   Computes the volume of the closed ball of radius r in the vector space K^n          s                                 q                                                                           q                                ,                       (              	                   $                                      +   /usr/local/magma-2.5/package/Code/entropy.m Py                                 q                                          z  
      	   __sig__19           {                                |           SpheresPackingBound         }                                               ~        5   Return true if C is a perfect code, else return false                                H                                                        
      	   __sig__20                                              
         VanLintBound d               f   Return the Hamming asymptotic upper bound of the information rate for delta in [0, 1] over the field K                               V    q                           V                       
      	   __sig__21                                             
      	   IsPowerOf                        |                                      '   /usr/local/magma-2.5/package/Code/bkb.m @        '   /usr/local/magma-2.5/package/Code/bkb.m @  
         __sig__0 ight Code                              0  P  h                   D                                      -   Computes the information rate of a given code   l	                           H                                 V           d  <  X  p    
         __sig__1   H  `          (   /usr/local/magma-2.5/package/Code/kraw.m    X	        R   Given a polynomial P over the Rational Field, return the polynomial Binomial(P, l)    d5                                                                                                        $    
      	   LeeWeight                        T                                      +   /usr/local/magma-2.5/package/Code/mattsol.m         +   /usr/local/magma-2.5/package/Code/mattsol.m X  
         __sig__1 nsform `    
         __sig__0   P  h             d   e         &      w   Return the inverse Krawchouk transform of the polynomial A over the rational field with respect to the vector space K^n 	  	  	                               q                                   <    0      
         __sig__3                     8                  
         __sig__1      	o6                                          KrawchoukPolynomial    0                                                   $      o   Return the Krawchouk transform of the polynomial a over the rational field with respect to the vector space K^n                                       q                                    $      `    
         __sig__2     P                               l	             KrawchoukTransform  
  
                                                            InverseKrawchouk         
         __sig__0                  BKBdsCardLargestLinearCode  x                                                     &      x   Return the best known bounds to the maximal minimum weight of a linear code of length n and dimension k over the field K     0    
         __sig__2     0             BKBdsCardLargestCode                                                         *         Compute the best known lowerand upper bounds to the cardinality of a largest linear code of length n and minimum weight d over the field K                                           q                                             
         __sig__1                                                       BinomialPolynomial    $                                                         Q   Return the Krawchouk polynomial of parameter k and n in K over the Rational Field                                        q                                       l                                   q                                                                                      BKBdsMaxMinimumWeight                                                              (   /usr/local/magma-2.5/package/Code/kraw.m    P        '   /usr/local/magma-2.5/package/Code/lee.m         8   Return the Lee weight of the vector v over a prime field      d5                         u                                            \  L  P                 L  X              $          ,   /usr/local/magma-2.5/package/Code/decodeml.m         >   Return a maximal set of equations orthogonal for each position  	                           H                                                                                                              __sig__1   `                   InverseMattsonSolomonTransform                                                           *   /usr/local/magma-2.5/package/Code/isproj.m  0         *   /usr/local/magma-2.5/package/Code/isproj.m  x         (   Return true iff the code C is projective         *         Given a, a polynomial over a finite field containing a primitive n-th root of unity, return the Mattson-Solomon transform of parameter n                                                                             |  l  p  p              l  x                             MattsonSolomonTransform                      t                                         __sig__0 omonTransform      ,         Given A, a polynomial over a finite field containing a primitive n-th root of unity, return the inverse Mattson-Solomon transform of parameter n                                                                            l    D                   4                                      '   /usr/local/magma-2.5/package/Code/lee.m P                         H                                        @0                                       d5  
         IsProjective                                                             (   /usr/local/magma-2.5/package/Code/bkab.m d5`        (   /usr/local/magma-2.5/package/Code/bkab.m    `  $      s   Return the best known asymptotic lower and upper bound of the information rate for delta in [0, 1] over the field K   d5                         V    q                           V V                      
         __sig__0   d5                                  	                                                               <  ,                       (              	          '   /usr/local/magma-2.5/package/Lat/code.m         '   /usr/local/magma-2.5/package/Lat/code.m         9   The lattice constructed from code C according to method S   d      
         BKABdsInfoRate  ~z2                                                 
         __sig__0 2.5/package        (   /usr/local/magma-2.5/package/Lat/genus.m P9\1        ,   /usr/local/magma-2.5/package/Code/decodeml.m `  
         __sig__0                        l                       <         Decoder for binary codes. Given a list of received vectors, return a two sequences. The second contains the corrected vectors, the first, boolean values saying if the decoder could retrieve the original codeword ,  D                          u    H                                                                             H                                      D  4  8        
         __sig__0                      4  @                         '   /usr/local/magma-2.5/package/Lat/cons.m  &     2   '   /usr/local/magma-2.5/package/Lat/cons.m  &           The sum of lattices L1 and L2                                                                     \  L  P        
         __sig__0      d5            L  X                         P   The direct sum of lattices L1 and L2 (with orthogonal sum of the inner products)                                                                           l  L  `  (    
         __sig__1                     L  h                          P   The direct sum of lattices L1 and L2 (with orthogonal sum of the inner products)                                                                           |  L  p       
         __sig__2 
                     L  x              0     
         OrthogonalSum     !                 t                              "        O   The direct sum of the lattices in Q (with orthogonal sum of the inner products)   Bz2    #                                                                -    L      $  
         __sig__3 z2       %            L                              
         DecodeML                                                              +   /usr/local/magma-2.5/package/Lat/standard.m &'        +   /usr/local/magma-2.5/package/Lat/standard.m &'        %   The standard lattice given by S and n     
  
         __sig__0       J           Density                                   K                                               L           The centre density of L       M                                                                    <  L  0    N  
      	   __sig__12       O            L  8                P  
         Return s * L     R        	   __sig__13           >  
         DualQuotient      ?                                               @        &   The p-neighbour of L with respect to v  
  A                                                                   L     0  B  
      	   __sig__10     0  C            L                          )   /usr/local/magma-2.5/package/Lat/lambda.m d5*p1           The laminated lattice of rank n                                                                               D  4  8       
         __sig__0                      4  @              $    
      	   DeepHoles                                                                  The covering radius of lattice L 	  	  8
                                                                         T         
         __sig__4                   T                @  %           MySort e     
         __sig__2                    T                P                                                            The deep holes of lattice L x                                                                           T    0    
         __sig__3   (  @              T                    (         The Voronoi cell of lattice L, as the vertices (a sequence of vectors), the set of edges, and the planes (a sequence of vectors)       p                                                                         p  T  d                  T  l                  
         VoronoiCell                         h                                         The Voronoi graph of lattice L        
         __sig__1            &        O   The direct sum of the lattices in Q (with orthogonal sum of the inner products)             '                                                                      L        (  
         __sig__4            )            L                    *        (   The tensor product of lattices L1 and L2            +                                                                3    L        ,  
         __sig__5            -            L                    .            The exterior square of lattice L            /                                                                       L        0  
         __sig__6            1            L                    2        !   The symmetric square of lattice L           3                                                                       L        4  
         __sig__7            5            L                    6           The dual Lattice of L       7                                                                 .    L        8  
         __sig__8            9            L                    :        ^   The dual quotient L#/L of L, together with the dual L# and the natural epimorphism f:L -> L#/L      ;                                                                         L        <  
         __sig__9            =            L                    Q                                                               T  L  L  @    S            L  H              	  T  
         Return L * s 
  
  U                                                                 \  L  P    V  
      	   __sig__14       W            L  X                D  
      	   Neighbour           E                                               F        (   The centre density of L, in real field K            G                                                             4  $  L        H  
      	   __sig__11           I            L                                LaminatedLattice                         <                                      (   /usr/local/magma-2.5/package/Lat/holes.m 
  @;p<     
   (   /usr/local/magma-2.5/package/Lat/holes.m   ;p<  
         DirichletVert                DirichletPlanes         
         __sig__0                  Holes   (  ~  
         MinkowskiMap                                                             4   Apply the Minkowski map to the element a of an order 
  
                                                                         L         
      	   __sig__26                   L                  X  
         Return L / s        Y                                                               t  l  L  `      Z  
      	   __sig__15           [            L  h                  \  
         Return L / s        ]                                                                   |  L  p      ^  
      	   __sig__16           _            L  x                  `        )   The ring of coefficients of the lattice L           a                                                                ^    L        b  
      	   __sig__17           c            L                    d  
         CoordinateRing      e                                               f        T   Apply Seysen reduction to L, returning a new lattice and the transformation matrix T        g                                                                        L        h  
      	   __sig__18           i            L                    j        R   Apply pair-reduction to L, returning a new lattice and the transformation matrix T          k                                                                        L        l  
      	   __sig__19           m            L                    n  &      x   A lattice with Gram matrix equal to L but with a diagonal inner product matrix,together with the transformation matrix T            o                                                                        L        p  
      	   __sig__20           q            L                    r        F   Apply the Minkowski map to the element a of the algebraic number field ith Es                                                                     L     u            L                dG|  
      	   __sig__24           v        X   A lattice with Gram matrix equal to L over real field K but with Euclidean inner product            w                                                                  L        x  
      	   __sig__22           y            L                    t        	   __sig__25                 z         b   A lattice with Gram matrix equal to L over the default real field but with Euclidean inner product          {                                                                       L        }            L                                                                                          T  |                T                	    
         VoronoiGraph 
  
                                                            The holes of lattice L                                                                           T        ,          (   /usr/local/magma-2.5/package/Lat/kappa.m    PJP        (   /usr/local/magma-2.5/package/Lat/kappa.m    JP           The Kappa lattice K_n                                                                            $            
         __sig__0                                               
         KappaLattice                                                               )   /usr/local/magma-2.5/package/Lat/lambda.m   8LP     B   *   /usr/local/magma-2.5/package/Lat/iterate.m  L`S  
         Nsforms            
         Naforms      d5  
         Ncenends                     EndomorphismRing    *   +              CentreOfEndomorphismRing    8   9     
         __sig__3 tricForms          F   The number of invariant (both symmetric and anti-symmetric) forms of G  Z              __sig__0    c   f   g   h   #            <                  D  
         __sig__7       E            <                  F  
         ReplacePrimes   	  G                                               H        .   Check the correctness of the soluble quotient.    I                         O                                           ,  <       J  
         __sig__8   ,    K            <  (                L  
         SQ_check       M                 $                              P  
         __sig__9       $  
      
   Initialize     8  %                                               &         f   Initialize a SQProc for a given quotient epi:F -> G without any information about the relevant primes.    Z  X      R                      !   "   #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   4   5   6   7   8   9   :   ;   <   =   >   ?   @   A   B   C   D   E   F   G   H   I   J   K   L   M   N   O   P   Q   R   S   T   U   V   W   8   X   Y   Z   [   \   ]   ^   _   `   a   b   c   f   g   h   i   j   k   l   m               ,   The number of symmetric invariant forms of G                               j                                          8    ,  $                4              <             AntisymmetricForms                                                              9   n invariant forms of G (either symmetric or antisymmetric     (                               j                                              
         __sig__6                                       
         __sig__7         
         InvariantForms                      `                                      R   The symmetric invariant forms of G (the first symmetric form is positive definite)                               j                                              t  h    
         __sig__4   `                  |              (             Data   T             NumberOfSymmetricForms  0                   0                                      1   The number of anti-symmetric invariant forms of G   H  t          *   /usr/local/magma-2.5/package/Lat/iterate.m  pXPh                            j                                             j                            d5k  
         Sublattices      l                                               m  &      }   The G-invariant sublattices of the natural lattice L of G which are not contained in p.L and whose index in L is a power of p d5    n                             j                                            o  
         __sig__1 d5       p                            	d5q        M   Representatives for the G-invariant sublattices of the natural lattice L of G      r                         j                                                0  s  
         __sig__2         t                                u  ,         The G-invariant sublattices of the G-lattice L which are not contained in p.L for any p in Q and whose index in L is a product of elements of Q          v                                                                          w  
         __sig__3      Zz2x                               y  $      r   The G-invariant sublattices of the G-lattice L which are not contained in p.L and whose index in L is a power of p       z                                                                           {  
         __sig__4      If3|                               }        B   Representatives for the G-invariant sublattices of the G-lattice L  '7    ~                                                                                                         j                                          h    \                    d                           a   n symmetric invariant forms of G (the first symmetric form is positive definite if n is non-zero)     	                               j                                                                        4          %   n anti-symmetric invariant forms of G                                  j                                  (        X  p      
         SymmetricForms                       x                                      '   The anti-symmetric invariant forms of G                                      j                                                      
         __sig__5                                            ?           CentralEndomorphisms      @                                               A        K   The centre of the endomorphism ring of the integral/rational matrix group G x    B                         j                                        H        0  C  
      	   __sig__26   (  @  D                              E           CentreOfEndomorphismRing     t      #  
         Endomorphisms      $                                               %        =   The endomorphism ring of the integral/rational matrix group G   (  &                         j                                                  '  
      	   __sig__20       (                              1  
      	   __sig__22 phismRing            Limits  p     
         __sig__8                                              
      	   __sig__12 ricForms          F   The number of invariant (both symmetric and anti-symmetric) forms of G                                                                                       
         __sig__9                                                    ,   The number of symmetric invariant forms of G                                                                                         
      	   __sig__10                                                   1   The number of anti-symmetric invariant forms of G                                                                                             
      	   __sig__11                                                     e   The symmetric and anti-symmetric invariant forms of G (the first symmetric form is positive definite)                                                                        8                                                    R   The symmetric invariant forms of G (the first symmetric form is positive definite)                                                                           H               
      	   __sig__13                                           	        '   The anti-symmetric invariant forms of G             
                                                                 X  0    $        
      	   __sig__14                         ,                          9   n invariant forms of G (either symmetric or antisymmetric                                                                              @    4        
      	   __sig__15                         <                           a   n symmetric invariant forms of G (the first symmetric form is positive definite if n is non-zero)                                                                              P    D        
      	   __sig__16                         L                          %   n anti-symmetric invariant forms of G                                                                          `    T        
      	   __sig__17                         \                             The Bravais group of G                               j                                 j           p    d        
      	   __sig__18                         l                    
         BravaisGroup                         h                                      ^   N independent endomorphisms from the endomorphism ring of the integral/rational matrix group G                                     j                                        |      !  
      	   __sig__19           "                                F                                               [        	   __sig__31 fEndomorphismRing G        \   The dimension of the centre of the endomorphism ring of the integral/rational matrix group G     H                         j                                        X  (        J              $                K        #   DimensionOfCentreOfEndomorphismRing @  X  )        N   The dimension of the endomorphism ring of the integral/rational matrix group G      *                         j                                                    +  
      	   __sig__21           ,                                -           DimensionOfEndomorphismRing         .                                               /        I   N independent endomorphisms from the endomorphism ring of the G-lattice L           0                                                                              2                                3        (   The endomorphism ring of the G-lattice L            4                                                                               5  
      	   __sig__23           6                                I  
      	   __sig__27 smRing ng 7        9   The dimension of the endomorphism ring of the G-lattice L           8                                                                               9  
      	   __sig__24           :                                ;         f   N independent central endomorphisms from the endomorphism ring of the integral/rational matrix group G      <                              j                                  8            =  
      	   __sig__25           >                                c  
         DimensionOfHom    d                                               e        )   /usr/local/magma-2.5/package/Lat/sublat.m   |~f        )   /usr/local/magma-2.5/package/Lat/sublat.m   |~g  .         The G-invariant sublattices of the natural lattice L of G which are not contained in p.L for any p in Q and whose index in L is a product of elements of Q      i  
         __sig__0       L                                                M        Q   N independent central endomorphisms from the endomorphism ring of the G-lattice L   
  
  N                                                                    @    4  `  O  
      	   __sig__28   P  h  P              <                Q        6   The centre of the endomorphism ring of the G-lattice L            1    Returns True if the ring map phi is surjective.    X                                                                     .    H    
    
         __sig__3                   H                                                                                         H        
         __sig__4     ,              H                x             Implicitization   @  `  R                                                                     P    D      S  
      	   __sig__29           T              L                  U        G   The dimension of the centre of the endomorphism ring of the G-lattice L             V                                                                     `    T      W  
      	   __sig__30           X              \                  Y        G   A non-trivial homomorphism from G1 to G2, or zero if one does not exist             Z                                                          D           p    d      \              l                  ]  
         Homomorphism        ^                 h                              _        4   The dimension of the homomorphism module Hom(G1, G2)        `                         j    j                                          |      a  
      	   __sig__32           b                                           JacobianSequence                                                               O   Returns the ideal generated by all first partial derivatives of the polynomial.                                                                                 h    
         __sig__1   `                                (    
         JacobianIdeal       
         __sig__2               &   /usr/local/magma-2.5/package/Mod/aut.m H           The automorphism group of M                               z                                 j       7  0     $        
         __sig__0      H6               ,                         +   /usr/local/magma-2.5/package/SeqEnum/sort.m PH        +   /usr/local/magma-2.5/package/SeqEnum/sort.m H        @   Sort the integer sequence Q using the diminishing increment sort d5                                X                                        P  H  8  <  d5  
         __sig__0                      8  D                          @   Sort the integer sequence Q using the diminishing increment sort    4                              X                                    `  X  8  L       
         __sig__1                      8  T              	          @   Sort the integer sequence Q using the diminishing increment sort                                   X                                  h  8  \        
         __sig__2      63            8  d                            Return true iff I equals J l/RingMaps.m  z2        0   /usr/local/magma-2.5/package/SeqEnum/eseq_misc.m    H        0   /usr/local/magma-2.5/package/SeqEnum/eseq_misc.m   ЍH            The join of all elements of S       -Z6                        0                                 0           p  t                 p  |                            The join of all elements of S                
         __sig__5                                                    *   /usr/local/magma-2.5/package/Mod/irrmods.m  P        *   /usr/local/magma-2.5/package/Mod/irrmods.m  P  @         Given a G-module M for a group G over a finite field, construct NumIrrs irreducible modules for G by forming tensor products of M and consequent irreducibles provided that the degree of a tensor product does not exceed DimLim                                        >                                                  
         __sig__0                                                    &   /usr/local/magma-2.5/package/Mod/aut.m P        .   /usr/local/magma-2.5/package/SetMulti/minmax.m ؙ            The minimum of the elements of S                                                                                         
         __sig__0                                                      The maximum of the elements of S    \                                                                                     
         __sig__1                                                /   /usr/local/magma-2.5/package/RngMPol/IdealOps.m ؙ        /   /usr/local/magma-2.5/package/RngMPol/IdealOps.m ؙ        H   Returns the sequence of all first partial derivatives of the polynomial. d5                                                                                  5  
         __sig__0                                           
         JacobianMatrix                     0                                      /   /usr/local/magma-2.5/package/RngMPol/RingMaps.m (     
   /   /usr/local/magma-2.5/package/RngMPol/RingMaps.m (        '   Display a map between polynomial rings.     0                                                                     X  H  L  t    
         __sig__0     t    
         DisplayPolyMap                                                     (         Returns the ideal generated by the partial derivatives of each polynomial in the sequence, by each indeterminate in its parent ring. 4                                                                    ^  (                      $                    
         __sig__3                                    0                                 0             p          
         __sig__1                        p                            .   /usr/local/magma-2.5/package/SetMulti/reduct.m P        .   /usr/local/magma-2.5/package/SetMulti/reduct.m P        6   The sum (counting multiplicities) of all elements of S                                                                                      
         __sig__0                                                    :   The product (counting multiplicities) of all elements of S                                                                                          
         __sig__1                                                    .   /usr/local/magma-2.5/package/SetMulti/minmax.m P        "   Return true iff I is a subset of J                                S    S                                  S              
         __sig__1      d5                                          Return the ideal I + J  $                           S    S                           S       X.              
         __sig__2                                                    Return the ideal I * J  d5                         S    S                           S       -              
         __sig__3   d5                                              Return the ideal I ^ n                                   S                           S       ,             
         __sig__4                                          (         Return the colon ideal I:J (or ideal quotient of I by J), consisting of the polynomials f of P such that f * g is in I for all g in J  3                             S    S                           S                      
         __sig__5 63                                   bz2	        -   Return the intersection of the ideals I and J       
                         S    S                           S       S  0    $       
         __sig__6                        ,              H          9   Return true iff I is not equal to the whole quotient ring   P                               S                                            @    4       
         __sig__7                        <              l          $   Return true iff I is a maximal ideal                                S                                            P    D        ,         Returns the matrix with (i,j)'th entry the partial derivative of the i'th polynomial in the list with the j'th indeterminate of its parent ring.                                                                     j       ^  8    ,                    4                    
         PolyMapKernel                      h                                      M    Returns True if the polynomial the_poly is in the image of the ring map phi.   `                                                                       H  |      
         __sig__2                   H                    
      	   IsInImage     $                                                                     H  T                                   P                                      E    Creates the kernel of a homomorphism "phi" between polynomial rings.                                                                            p  H  d        
         __sig__1                        H  l                  [           GaussianIntegerRing      \                 `                              ]        M   The ring of Gaussian integers (the maximal order of the quadratic field Q(i))     ^                                                                          X  t  0  _  
         __sig__1   (  @  `            X  |                a           GaussianIntegers   l    b                 x                                                                                             (   /usr/local/magma-2.5/package/HC/jac_hc.m -ʸ        :   /usr/local/magma-2.5/package/RngMPolRes/AffineAlgebraOps.m   x         :   /usr/local/magma-2.5/package/RngMPolRes/AffineAlgebraOps.m  Xx                         S    S                                  <A        t    
         __sig__0     t                              \  t      D          Assumes that phi is a parametrization of a variety defined by equations y_i = f_i(x_i) where the x_i are in the CODOMAIN of phi and the y_i are in the DOMAIN of phi. Returns the smallest variety containing the points defined by these equations.       k  
         __sig__3 Ring     c        V   The ring of Eisenstein integers (the maximal order of the quadratic field Q(Sqrt(-3)))  	  d                                                                          X      e  
         __sig__2   |    f            X                  i        V   The ring of Eisenstein integers (the maximal order of the quadratic field Q(Sqrt(-3)))    l            X                  2        '   /usr/local/magma-2.5/package/Rng/comp.m 3        *   The completion of field K at prime ideal P       4                                                                           6                              7        $   The completion of R at prime ideal P d5    8                             P                                              9  
         __sig__1 d5       :                            d5;        '   /usr/local/magma-2.5/package/Rng/frac.m <        '   /usr/local/magma-2.5/package/Rng/frac.m =        6   The fraction field R/I where I is a maximal ideal of R  (  >                                                                            ?  
         __sig__0    h      @                               A        6   The fraction field R/I where I is a maximal ideal of R 6    B                                                                         C  
         __sig__1 z2       D                            Zz2E        6   The fraction field R/I where I is a maximal ideal of R    F                                                                              G  
         __sig__2      uz2H                               I        &   /usr/local/magma-2.5/package/Rng/loc.m J        &   /usr/local/magma-2.5/package/Rng/loc.m K        &   The localization of R at prime ideal P      L                                                               H  8  (  ,     M  
         __sig__0          N            (  4              l  O  
         Localization      P                 0                              Q        &   The localization of R at prime ideal P      S  
         __sig__1              
         __sig__8                          L                          $   Return true iff I is a primary ideal                                 S                                            `    T        
         __sig__9                          \                             True iff the ideal I is radical                                      S                                            p    d        
      	   __sig__10                         l                          "   Return whether I is the zero ideal                                   S                                        .      t        
      	   __sig__11                          |                  !  p        Given an ideal I of a quotient ring P=R[x_1, ..., x_n] / J, where J is an ideal of R[x_1, ..., x_n], with coefficient ring R, together with a ring S, construct the ideal J of the polynomial ring Q=S[x_1, ..., x_n]/J obtained by coercing the coefficients of the elements of the basis of I into S. It is necessary that all elements of the old coefficient ring R can be automatically coerced into the new coefficient ring S        "                            S                           S                     #  
      	   __sig__12           $                                %           The radical of I            &                         S                                 S                     '  
      	   __sig__13           (                                5  
         __sig__0 ion        )        $   The primary decomposition of ideal I        *                         S                                                       +  
      	   __sig__14           ,                                -  "      l   The (prime) decomposition of the radical of I; note that this may be different to the associated primes of I        .                         S                                                       /  
      	   __sig__15           0                                1        '   /usr/local/magma-2.5/package/Rng/comp.m PV        *   /usr/local/magma-2.5/package/RngInt/misc.m  0W        M   The ring of Gaussian integers (the maximal order of the quadratic field Q(i))     X                                                                        h  X  \      Y  
         __sig__0      d5Z            X  d                            ThueSolveInexact                                                                                                                       H  @    4      
         __sig__2                     <                  "      g   True and an order whose defining polynomial is better, or false if such a polynomial could not be found     $                                                                    X  P    D    j                                                                          X      n                                               o  "      j   The integer nearest to x (rounded towards infinity) if x real; otherwise the nearest Gaussian integer to x      p                         V                                            X    (  q  
         __sig__4   l    r            X                    "      m   True and a number field whose defining polynomial is better, or false if such a polynomial could not be found                                                                       8  (      d    
         __sig__1   \  t                $                           BetterPolynomial                                                         "      m   True and a number field whose defining polynomial is better, or false if such a polynomial could not be found     g           EisensteinIntegerRing X5    h                                               m           EisensteinIntegers          R                                                                   P  (  D      T            (  L                  U        *   /usr/local/magma-2.5/package/RngInt/misc.m  8Py        [   Returns the solutions of |f(x,y)| = a, where f is the homogeneous form of the Thue object T      z                             B                                                  .         Input: a finitely generated free group F and two finitely generated subgroups H1 and H2; Output: the subgroup of F which is the intersection of H1 and H2   
  
                           "    "    "                     "           @    4  `    
         __sig__1   P  h                <                  
         FGIntersect   (                   8                                
         __sig__2   t      
      	   MultiRank   t            *   /usr/local/magma-2.5/package/FldNum/conv.m          *   /usr/local/magma-2.5/package/FldNum/conv.m          T   The number field L corresponding to the quadratic field K, and the map taking K to L                              @                                                                               (          U   The number field L corresponding to the cyclotomic field K, and the map taking K to L   <    
         __sig__3                       L                    "      g   True and an order whose defining polynomial is better, or false if such a polynomial could not be found      If3                                                                    `    T       
         __sig__4   '7                  \                        H   Returns a list with all possible fields L such that L = K1 K2 might hold    4                                                                         p    d       
         __sig__5                        l                  
         MergeFields                       h                                
         __sig__0            s        !   The nearest Gaussian integer to x           t                         F                                              X        u  
         __sig__5            v            X                    w        0   /usr/local/magma-2.5/package/FldNum/anf_compat.m x        0   /usr/local/magma-2.5/package/FldNum/anf_compat.m   h                                  
         __sig__9            {           The base 10 representation of n             |                                                                       X        }  
         __sig__7            ~            X                               __sig__0                         ,   The number whose base 10 representation is Q                                                                              X                    X                            ,   /usr/local/magma-2.5/package/FldNum/isprim.m            True iff a generates the field 5                                                                                 
         __sig__0 6                                   d5           True iff a generates the field  d5                         A                                                     
         __sig__1   d5                                          E   True iff element a of order O generates the field of fractions over Q                                                                                 d5  
         __sig__2       0                                          -   /usr/local/magma-2.5/package/FldNum/subflat.m         -   /usr/local/magma-2.5/package/FldNum/subflat.m         6   The intersection of the subfield lattice elements of Q 6                                                                                
         __sig__0 z2                                   63        *   /usr/local/magma-2.5/package/Cop/univmap.m           *   /usr/local/magma-2.5/package/Cop/univmap.m  h        (   The universal map from C to S given by Q                                         e                                      H    
         __sig__0                                           
         UniversalMap   <R'4                                                        -   /usr/local/magma-2.5/package/AlgFP/groebner.m         -   /usr/local/magma-2.5/package/AlgFP/groebner.m                          "    "    "                               (            
         __sig__0                        $                   
         PerfectGroup package                 p                                $      o   Return the perfect group in the database which is the nth extension of a group of order p^exp by the group base D  \  t                                                      "             h        
         __sig__1                   h                (          M   Return the simple or quasisimple perfect group in the database with name name                CosetGraphIntersect                                                                                                                                       
         __sig__1                                                    ,   /usr/local/magma-2.5/package/FldNum/isprim.m P                                                          "               h         
         __sig__2                      h                    
         __sig__4 sentation          ^   Represent the group G by forming a subdirect product of the coset actions on the subgroup in H 5                            "    "                                         h        
         __sig__3 d5                   h                d5        1    Compute largest possible soluble quotient of F.    X                             "                                           P  (      
  	  
         __sig__1       
              $                           __sig__6             4          4   /usr/local/magma-2.5/package/GrpFP/solquot/sq_proc.m         4   /usr/local/magma-2.5/package/GrpFP/solquot/sq_proc.m   
         SplitExt    q   r              ModulCandidates        __si         e   The set of primes p for which a non-trivial p-extension by Q exists in the database of perfect groups                                                                            h                    h                  '                                                          O          <      (  
         __sig__1 	  X	  p	  )            <                
  *        K   Initialize a SQProc for a finitely presented group F with expected order n. |    +                             "                           O          <      ,  
         __sig__2     (  -            <                x  .        J   Initialize a SQProc for a given quotient epi:F -> G with expected order n.                  PerfectGroupExtensions                                                            U   The set of tuples <n1, n2> such that Q#p(n1, n2) is is the database of perfect groups   >2                                                                     h                   Series        l        Input: a finitely generated free group F and two finitely generated subgroups H1 and H2; Output: a coset graph CG for the intersection of H1 and H2. This graph is the component of the graph CG1xCG2 which includes the vertex (1,1) (where CG1, CG2 are the coset graphs of H1, H2 respectively). The vertex labels of CG are minimal with respect to the Shortlex ordering with regard to the generators of F                             P                                      4   /usr/local/magma-2.5/package/GrpFP/perfgps/perfgps.m @        4   /usr/local/magma-2.5/package/GrpFP/perfgps/perfgps.m       $      o   Return the perfect group in the database which is the nth extension of a group of order p^exp by the group base @  `                                                      "           x  h  l      
         __sig__0   <  \              h  t                ,  D    0         Input: a finitely generated free group F and two finitely generated subgroups H1 and H2; Output: the expression computed for the generalized Hanna Neumann conjecture                                "    "    "                               X    L                    T                              h                              PerfectGroupClass     P                                                          /   /usr/local/magma-2.5/package/GrpFP/solquot/sq.m         /   /usr/local/magma-2.5/package/GrpFP/solquot/sq.m   .          Compute a soluble quotient of F. P is a set of primes and the algorithm calculates the largest quotient such that the order has prime divisors only in P.  "                                                   8                           PerfectGroupRepresentation  x                                                           ?   The set of base groups stored in the database of perfect groups                                                                                 h    h              h                             PerfectGroupBases   H  t                                                   
         __sig__6 sions  <             __sig__5   ,  D  \  |  
        ,   Algebraic relations for the invariant ring R       
                                                                     H(  0(  <(  4  
            0(  D(              L  
        9   The ideal of algebraic relations for the invariant ring R        
                                                                     X(  0(  L(    
  
         __sig__1        
            0(  T(                
        )   /usr/local/magma-2.5/package/FldFun/pfd.m   
        )   /usr/local/magma-2.5/package/FldFun/pfd.m   X'
           LCM of elements of Q mposition  @  
        =   The (complete) squarefree partial fraction decomposition of f   l  
                         Q                                            p(  `(  d(  H  
  
         __sig__0      l  !
  
         __sig__1        <  
      	   AddPrimes       =                                               >        E   mp is a set of primes which are added to the relevant primes for SQP.   (  ?                            O                                      <      @  
         __sig__6       A            <                   B        ;   Replace the set of relevant primes in SQP by the given set.     C                            O                                      <      /                                                        O            <        0  
         __sig__3      <R'41            <                   2        -   Calculate the set of relevant primes for SQP.      3                        O                                          <    14  
         __sig__4       D  5            <                    7                                               8        2   Add the given prime to the set of relevant primes. 5       9                            O                                    <    1:  
         __sig__5       d  ;            <                    k                             "                           O           <      l  
      	   __sig__14   X	  p	  m            <                
  n  (         Start the soluble quotient algorithm for a finitely presented group F with relevant primes restricted by the sequence of tuples f.      o                             "                           O           <      p  
      	   __sig__15       q            <                  t  
      	   __sig__16       ~  
      	   __sig__18   d  |                               "                                         4    0                 __sig__7                            Collect p   q   r   s   t     
         NonsplitExt <p, e>,         
   n   o   p   q   r   s   t   u   v   w          "      g   Initialize a SQProc for a finitely presented group F without any information about the relevant primes.             !                         "                                 O          <        "           __sig__0                   "      j    Compute a soluble quotient of F with order n. If n is 0, then compute largest possible soluble quotient.                                        "                                       X    L        
         __sig__5                          T                                               "                                     ,              H          Compute a soluble quotient of F. S is a sequence of tuples <p, e>, with p a prime or 0 and e a non-negative integer. The order of the quotient will be a divisor of &* [ p^e : <p, e> in S] if all p's and e's are positive. See handbook for further details.             e	        +   /usr/local/magma-2.5/package/AlgChtr/chtr.m pf	  :         Remove occurrences of the irreducibles in Irr from the characters in Chs and look for new irreducibles in the reduced set. Return a sequence of new irreducibles found and the sequence of reduced characters   $  g	                        J   J                                       %  %  %      i	            %  %                	           The n-th odd graph O_n  $  	                                                          a            &  &  &  	  	  
         __sig__0 
  
  
  	            &  &              D  	  
         OddGraph     4  	                 &                              	            The triangular graph T_n (n > 1)   ,    	                                                          a           8&  &  ,&  `  	  
         __sig__1     0  	            &  4&                	  
         TriangularGraph l  	                 0&                              	           The n-th square lattice graph   "  	  
         __sig__2 #  #  #  	            &  L&              %  %  %  t	                                                                 %  %  %          v	            %  %                	  
         ClebschGraph     	                 x&                              	           The Shrikhande graph 	  	  	                                                             a           &  &  &    	  
         __sig__5   |    	            &  &                	  
         ShrikhandeGraph   	                 &                              	        &   The sequence of the three Chang graphs  `  	                                                                        &  &  &  L  	  
         __sig__6       	            &  &              <!  	  
         ChangGraphs 4"  \"  	                 &                              	           The Gewirtz graph   %  %  %  (&  w	           CharacterDegrees       @  x	                 %                              X           IntersectKernels        Y                 T                              Z  6         Compose the lifts SQ1 and SQ2 of SQP to a new bigger quotient. If the optional parameter Check is set to true, it will be tested whether the intersection of the kernels has maximal index. P  h  [                         O   O   O                     O          t  <  h    \  
      	   __sig__11       ]            <  p                ^           ComposeQuotients   ,  D  x        	   __sig__17 cess    0  H  N  6         Checks whether two soluble quotients have the same kernel. If not and Construct is true, then a bigger quotient will be constructed, where the kernel is the intersection of both kernels.          O                         O   O                           O          D  <  8      Q            <  @                  R           EquivalentQuotients         S                 <                              T  6         Construct a bigger soluble quotient by intersecting the kernels of the given quotient. The return values are a new soluble quotient process and maps from the new to the given soluble groups.      U                         O   O                          O            \  <  P      V  
      	   __sig__10           W            <  X                  d           SolubleQuotientProcess     e                                               f  $      r   Start the soluble quotient algorithm for a finitely presented group F with expected order of the quotient being n.      g                             "                           O           <    @  h  
      	   __sig__13       i            <                T  j  ,         Start the soluble quotient algorithm for a finitely presented group F with expected order of the quotient being the factorized integer f.   0  H  `  x  _                 l                              `  &      x   Start the soluble quotient algorithm for a finitely presented group F without any information about the relevant primes.            a                         "                                 O           <        b  
      	   __sig__12           c            <                      
         AppendModule                                                      
      
    internal   T	  l	                                           O                      <    p    
      	   __sig__27   H  `              <                    
         SolutionSpace                                                                                 O                                     <        
      	   __sig__28                   <                  0  h    
         SplitCollector                      $                                ,         Setup the collector for a standard ssplit extension of SQP with algebra RG, R the prime ring in characteristic p. ws defines the weights of a series.   `                                  O                          L  D  <  8      
      	   __sig__22                   <  @                                                    O                        T  <  H            	   __sig__23   `  x      r  $      s   Start the soluble quotient algorithm for a finitely presented group F with relevant primes restricted by the set s.         s                             "                           O             <        u            <                    v  "      k   Set up the collector for a nonsplit extension of SQP with algebra RG, R the prime ring in characteristic p.         w                            O                                    <        y            <                    z           NonsplitCollector           {                                               |  ,         Set up the collector for a nonsplit extension of SQP with algebra RG, R the prime ring in characteristic p. The pairs in tr indicates trivial tails.        }                                O                              <                    <                      6         Set up the collector for a nonsplit extension of SQP with algebra RG, R the prime ring in characteristic p. The pairs in tr indicates trivial tails. ws defines the weights of a series.                                                O                        <           
      	   __sig__19                       <                      B         Set up the collector for a nonsplit extension of SQP with algebra RG, R the prime ring in characteristic p. The pairs in tr indicates trivial tails. ws defines the weights of a series. epi is an epimorphism onto another soluble group.                                                  O                    <          
      	   __sig__20                       <                      $      q   Set up the collector for a standard split extension of SQP with algebra RG, R the prime ring in characteristic p.                                       O                                <  ,  <           
      	   __sig__21                       <  (                    4          Calculates the split extension lift for the module M. The return is -1 iff the solution space does not exist in general,otherwise it is the Fq-dimension of the space (could be 0).   d             SplitExtensionSpace                                                      :          Calculates the split extension lift for the modules in the list. Returned is a sequence of: -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).   0    
      	   __sig__29                    <                l    8         Set up the collector for a nonsplit extension of SQP with algebra RG, R the prime ring in characteristic p. ws defines the weights of a series. epi is an epimorphism onto another soluble group.                       <  P                    6         Calculates the G-modules in characteristic p with respect to the given options. The return value is 0 iff no such module exists, otherwise it is the index of the list of modules in SQP.                                        O                                 t  d  <  X        
      	   __sig__24                       <  `                                   \                                      7   Calculates the modules for all (known) relevant primes.                                      O                                           |  <  p        
      	   __sig__25                       <  x                             image        T      4  Append/Find the module M in the list of modules in SQP. The first return value is the index of the module in the char p list in SQP. The second return value is false iff the index belongs to an isomophic module. (It might happen that the isomorphism is the identity; relevant is the internal data structure.)                                     O                                        <          
      	   __sig__26                       <                               DeleteSplitSolutionspace   H  `                   d                                      X   Delete the k-th split solution space of the i-th p-module as the actual solution space.    (  @                                      O                          <  x      
      	   __sig__39                   <                             DeleteNonsplitSolutionspace ,  t                   |                                                                   O              O          <                                   O                                     <        >          Calculates the split extension lift for the modules in the l-th list in SQP. The return is a sequence of: -1 iff the solution space does not exist in general,otherwise it is the Fq-dimension of the space (could be 0).  (  @                                   O                               <    t    
      	   __sig__30                   <                ,    
      	   __sig__31                   <                h        &      z   Build the split extension of the i-th p-module for the k-th solution space. A set of linear combinations can be specified.  	  	              <                ,             LiftSplitExtension  \  t                                                         X   Build the split extension of the l-th list of p-modules for their actual solution space.                                        O                     O          <        
      	   __sig__41   `                <                |             IsNode Pl     <          Calculates the split extension lift for the p-modules stored in SQP. The return is a sequence of: -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).                                      O                                     <          @          Calculates the split extension lift for all modules stored in SQP. The return are sequences for each prime of: -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).                                     O                                             <          
      	   __sig__32                       <                       
      	   __sig__40 tionspace   6          Calculates the nonsplit extension lift for the module M. The return is -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).                                         O                                 $    <          
      	   __sig__33                       <                               NonsplitExtensionSpace                                                       <         Calculates the nonsplit extension lift for the modules in the list. The return is a sequence of: -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).                                        O                                 4  ,  <           
      	   __sig__34                       <  (                    >         Calculates the nonsplit extension lift for the modules in the l-th list in SQP. The return is a sequence of: -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).                                        O                           D  <  <  0        
      	   __sig__35                       <  8                    <          Calculates the split extension lift for the p-modules stored in SQP. The return is a sequence of: -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).                                      O                                 T  L  <  @        
      	   __sig__36                       <  H                    @          Calculates the nonsplit extension lift for all modules stored in SQP. The return are sequences for each prime of: -1 iff the solution space does not exist in general, otherwise it is the Fq-dimension of the space (could be 0).                                  O                                           \  <  P        
      	   __sig__37                       <  X                          X   Delete the k-th split solution space of the i-th p-module as the actual solution space.                                                 O                        l  <  `        
      	   __sig__38                       <  h                             LiftNonsplitExtension      	                                                &  
      	   __sig__54 ionRow 	  
        \   Build the non-split extension of the l-th list of p-modules for their actual solution space.                                       O                     O      <   4   <  (       
      	   __sig__48     (              <  0               t          W   Build the non-split extension of the list of p-modules for their actual solution space. |        
      	   __sig__49   `  x              <  @                         S   Build the split extension of the list of p-modules for their actual solution space.                                  O                           O          <        
      	   __sig__42                   <                          Q   Build the split extension of the list of modules for their actual solution space.   H  t                           O                                 O            <    <    
      	   __sig__43   ,  D              <                H                               O                           O      L   D   <  8   d          U   Build the non-split extension of the list of modules for their actual solution space.   <
                           O                                 O          T   <  H       
      	   __sig__50                   <  P               D    "      i   Build the non-split extensions of SQP for the p-modules in the l-th list for their actual solution space.                                        O                     O      t   d   <  X       
      	   __sig__51   4  l             flexes              e   Build the split extensions of SQP for the p-modules in the l-th list for their actual solution space.                                        O                     O          <          
      	   __sig__44                       <                               LiftSplitExtensionRow                                                              \   Build the split extensions of SQP for the list of p-modules for their actual solution space.                                     O                           O           <          
      	   __sig__45                       <                             Q   Build the split extension of the list of modules for their actual solution space.                                    O                                 O             <            
      	   __sig__46                       <                       &      ~   Build the non-split extension of the i-th p-module for the k-th solution space. A set of linear combinations can be specified.                                           O              O      ,      <           
      	   __sig__47                       <                     8  
         PrintSeries     9                                                :  
         Print function  l	  ;                        O                                             <     p  <  
      	   __sig__58   H  `  =            <                   >  
         PrintPrimes     ?                                                @  
         Print function    A                        O                                      !  !  <   !    B  
      	   __sig__59   `  x  C            <  !                (  
         PrintProcess      )                                                *        "   General print function for SQProc.  `
  
  +                        O                                             <     0  ,  
      	   __sig__55     0  -            <                   .  
         Print function    /                        O                                             <     \  0  
      	   __sig__56     ,  1            <                   2  
         PrintQuotient   h  4  
         Print function  h               <  `                              LiftNonsplitExtensionRow                             \                                        `   Build the non-split extensions of SQP for the list of p-modules for their actual solution space.                                         O                           O         |   <  p         
      	   __sig__52                       <  x                            U   Build the non-split extension of the list of modules for their actual solution space.       !                         O                                 O             <         "  
      	   __sig__53           #            <                     $        <   Print function for SQProc. Print prime specific information.        %                            O                                      <         '            <                     P  
         Print function    Q                        O                                      \!  L!  <  @!  p	  R  
      	   __sig__62   
  
  S            <  H!                T  
         PrintModules     U                 D!                              V  
         Print function    W                            O                                    d!  <  X!    X  
      	   __sig__63   x    Y            <  `!              H  Z  
         Print function    \  
      	   __sig__64       ^  
         PrintExtensions    3                                                5                        O                                             <         6  
      	   __sig__57           7            <                     [                        O                                      !  t!  <  h!    ]            <  p!              	  _                 l!                              `  
         Print function    a                            O                                    !  <  !  @  b  
      	   __sig__65       c            <  !              T  d        7   Returns the soluble group and the epimorphism from SQP. <  l    e                         O                                            !  <  !  h  f  
      	   __sig__66       h   D  
         PrintCollector     E                 !                              F  
         Print function  	  G                            O                                    $!  <  !    H  
      	   __sig__60   x    I            <   !                J  
         Print function    K                        O                                          4!  <  (!  t  L  
      	   __sig__61     <  M            <  0!              |  N  
      
   PrintRelat  0  H  O                 ,!                                          <  ("              $             DeleteSplitCollector   T                   L"                                      +   Delete all collectors for split extensions.                             O                                          l"  <  `"      
      	   __sig__75                   <  h"              x          B   Delete the collector for non-split extensions in characteristic p.  x                                O                                "  |"  <  p"  |    
      	   __sig__76   t                <  x"              |!  h  
         GetQuotient     i                 !                              j        P   Return the relevant primes stored in SQP and a flag indicating the completeness.   x    k                         O                                            !  <  !  0  l  
      	   __sig__67   (  @  m            <  !                n  
      	   GetPrimes   <  T  o                 !                              p        G   Returns the parent of SQP, i.e. the soluble Quotient which lifts to SQP   0  H  r  
      	   __sig__68       s            <  !              8!  P!  x!  g            <  !                  t  
      	   GetParent       u                 !                              v        ;   Returns a list of soluble quotients which are lifts of SQP. 
  
  w                         O                                           !  <  !    x  
      	   __sig__69       y            <  !                z  
         GetChildren H  t  {                 !                              |        9   Returns the i-th soluble quotient which is a lift of SQP.   \  |  }                             O                                     !  <  !  h   ~  
      	   __sig__70   !  !  q                         O                                O          !  <  !        
         GetChild                        !                                      '   Return the i-th p-module stored in SQP. 8
  `
  
                                   O                    z           "  <  "  0    
      	   __sig__71     0              <  "                  
      	   GetModule   (                     "                                      /   Return the list of all p-modules stored in SQP.     ,                               O                                 <"  ,"  <   "      
      	   __sig__72         <           Ambient Sys             <  !                             DeleteNonsplitCollector                     t"                                      /   Delete all collectors for non-split extensions. 
  
  
                          O                                          "  <  "      
      	   __sig__77                   <  "                        *   Delete the collectors in characteristic p.  l                                O                                "  "  <  "                <  "                  
         DeleteCollector                    "                              [           Finite ants   
      
   GetModules                        $"                                      0   Return the l-th list of p-modules stored in SQP. 
  
  
                                   O                               D"  <  8"      
      	   __sig__73                   <  @"                  
      	   __sig__78 ector t          >   Delete the collector for split extensions in characteristic p.  \                              O                                d"  T"  <  H"  H    
      	   __sig__74                   <  P"              8!             KeepSplitAbelian                         #                                (         Return the sequence useful for the Collector setup. It determines that the presentation of SQP and of SQR SQP are kept unchanged.                                 O   O                                     #  <  #      
      	   __sig__91     (              <  #              t             KeepSplitElementaryAbelian  t                     #                                      M   Return a sequence of pairs [j,i] s.t. the order of both G.j and G.i is not p.                                   O                                     #  <  #  #    
         DeleteProcess                       "                                      /   Delete the Process and all its child processes. 
  
  
                         O                                          "  <  "      
      	   __sig__81                   <  "                           DeleteProcessDown                        "                                
      	   __sig__83 ete             >   Delete all soluble quotient processes which are related to SQP  x                         O                                          "  <  "  !          !   Delete all the collectors of SQP.                                   O                                          "  <  "        
      	   __sig__79                       <  "                          -   Delete the soluble quotient process variable.                              O                                          "  <  "        
      	   __sig__80                       <  "                             DeleteProcessComplete   $                   "                                (         Return the sequence useful for the Collector setup. It determines that the order of the pc generators in SQP is kept unchanged.                                O   O                                     #  <  #                <  #              x             KeepGeneratorOrder                       #                                *         Return the sequence useful for the Collector setup. It determines that the conjugation action of the pc generators in SQP is kept unchanged. !  <!    
      	   __sig__84   4"  \"    
      	   __sig__82                       <  "                             KeepGeneratorAction   $                   $#                                (         Return the sequence useful for the Collector setup. It determines that the order of the pc generators in SQRSQP is kept unchanged.                               O   O                                     D#  <  8#      
      	   __sig__85     ,              <  @#              x    
         KeepElementary                     <#                                ,         Return the sequence useful for the Collector setup. It determines that the conjugation action of the pc generators in SQR SQP is kept unchanged. "  4"  \"                           O   O                                     ,#  <   #                  <  (#                    
         KeepAbelian                      T#                                0         Return the sequence useful for the Collector setup. It determines that the conjugation action of the pc generators of SQP on those of SQR SQP is kept unchanged.   |                             O   O                                     t#  <  h#      
      	   __sig__87     (              <  p#              x    
         KeepGroupAction @                   l#                                $      q   Return the sequence useful for the Collector setup. It determines that the presentation of SQP is kept unchanged.   "  "    
      	   __sig__88   4#  L#                           O   O                                     \#  <  P#        
      	   __sig__86                       <  X#                    
      	   KeepSplit                        #                                
      	   __sig__92 yAbelian    .         Return the sequence useful for the Collector setup. It determines that the order and the conjugation action of the pc generators in SQR SQP is kept unchanged.  l                           O   O                                     #  <  #      
      	   __sig__89                   <  #                           KeepElementaryAbelian   H                   #                                                       O   O                                     #  <  #  "          	   __sig__90   4#  L#  d#  |#                           O   O                                     #  <  #                  <  #                              <  #              $  	  
      	   __sig__94       	            <  $              @	  	            <  @$              
  	  
      	   __sig__99 ection   	        T   Determine the maxinmal p-elementary abelian module which lifts to a bigger quotient.     	                             O                           O      d$  T$  <  H$  (  	  
      	   __sig__97        	            <  P$              @  	           ElementaryAbelianSection       	                 L$                              	                         O                                 O          l$  <  `$  "  	  
      	   __sig__98   #  #    .         Return the sequence useful for the Collector setup. It determines that the presentation of SQP and the conjugation action in SQR SQP are kept unchanged.                        <  #                  	  
         IsPureOrder     		                 $                              
	        H   Determine the maximal p-abelian module which lifts to a bigger quotient.   H  `  	                             O                           O      <$  4$  <  ($    	  
      	   __sig__95       	            <  0$                	  <         Determine the maximal abelian module which lifts to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.   h  	                         O                                 O          D$  <  8$  X"  	  
      	   __sig__96   `#  x#    
         KeepPrimePower                      #                                *         Return a sequence of pairs [j,i] correspnding to the weight condition for the p-group. The weights are defined by the sequence of quotients.   0                                                                       $  <  #     	  
      	   __sig__93   H  t  	            <   $                	           KeepPGroupWeights   t    	                 #                              	        5   Check the PC presentation of G for the Hall property.     	                                                                       $  <  $  #  y	                                                                 %  %  %        {	            %  %              	  |	                                                                  &  %  %        }	  
         __sig__2   x    ~	            %  %                	  &      |   The sequence [C_0, C_1, ...] where C_i is the number of irreducible characters of G with degree p^i for the finite p-group G     	                         j                                            &  %  %    	  
         __sig__3   0  h  	            %  &                 	        +   /usr/local/magma-2.5/package/Graph/graphs.m (М	        +   /usr/local/magma-2.5/package/Graph/graphs.m pМ 	  
         SplitSection      !	                 t$                              "	  @         Determine the maximal nilpotent group with a splitting lift to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.   `    #	                         O                                 O          $  <  $    $	  
      
   __sig__100  <  \  %	            <  $                &	        R   Determine the maximal p-abelian module with a splitting lift to a bigger quotient.      '	                             O                           O      $  $  <  $  H#  (	  
      
   __sig__101   $  X$  	  @         Determine the maximal elementary abelian module which lifts to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.            	            <  h$                  	        I   Determine the maximal p-group with a splitting lift to a bigger quotient.           	                             O                           O      $  |$  <  p$      	            <  x$                  4	           SplitElementaryAbelianSection   d  5	                 $                              6	  B         Determine the maximal elementary abelian group with a splitting lift to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.       7	                         O                                 O          $  <  $  x  8	  
      
   __sig__104    @  9	            <  $                :	        M   Determine the maximal p-group with a non splitting lift to a bigger quotient.   l   ;	                             O                           O      %  $  <  $  |#  <	  
      
   __sig__105  $  $  )	            <  $                  *	           SplitAbelianSection         +	                 $                              ,	  >         Determine the maximal abelian group with a splitting lift to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.      -	                         O                                 O          $  <  $      .	  
      
   __sig__102          /	            <  $                  =	            <  $                  0	        ^   Determine the maxinmal p-elementary abelian module with a splitting lift to a bigger quotient.      1	                             O                           O      $  $  <  $      2	  
      
   __sig__103          3	            <  $                  H	           NonsplitAbelianSection  $  I	                 %                              J	  B         Determine the maximal elementary abelian group with a splitting lift to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.       K	                         O                                 O          4%  <  (%    L	  
      
   __sig__108  x    M	            <  0%              H  Z	        
   __sig__111 belianSection   N	        ]   Determine the maximal p-elementary abelian module with a splitting lift to a bigger quotient.   "  Q	            <  @%              |#  V	        
   __sig__110  $  $  $  $  >	  
         NonsplitSection     ?	                 $                              @	  B         Determine the maximal elementary abelian group with a splitting lift to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.           A	                         O                                 O          %  <   %      B	  
      
   __sig__106          C	            <  %                  P	  
      
   __sig__109 ion      D	        V   Determine the maximal p-abelian module with a non splitting lift to a bigger quotient.      E	                             O                           O      ,%  %  <  %      F	  
      
   __sig__107          G	            <  %                  \	  
         pSection       ]	                 d%                              ^	  P         Determine the maximal nilpotent group with a lift to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account. Steps puts a limit on the weights of the p-groups of the nilpotent group.   L  x  _	                         O                                 O          %  <  x%  @  `	  
      
   __sig__112  0  H  a	            <  %              L  b	           NilpotentSection   t    c	                 |%                              d	        +   /usr/local/magma-2.5/package/AlgChtr/chtr.m 0h	  
         __sig__0 $  $%  L%  O	                             O                           O      T%  D%  <  8%      R	            NonsplitElementaryAbelianSection            S	                 <%                              T	  B         Determine the maximal elementary abelian group with a nonsplitting lift to a bigger quotient. If PrimeCalc equals true, the relevant primes will be calculated first. If ModuleList is 0, only the known modules will be taken into account.        U	                         O                                 O          \%  <  P%      W	            <  X%                  X	        C   Determine a lift with a p-group, given by its lower central series.         Y	                             O                           O          l%  <  `%      [	            <  h%                  j	           RemoveIrreducibles    $  k	                 %                              l	  4         Make the norms of the characters in Chs smaller by computing the differences of appropriate pairs. Return a sequence of new irreducibles found and a sequence of reduced characters   4  m	                        J   J                                       %  %  %  x  n	  
         __sig__1     x  o	            %  %              `  p	           ReduceCharacters   x    q	                 %                              r	        +   /usr/local/magma-2.5/package/AlgChtr/pgps.m   s	        +   /usr/local/magma-2.5/package/AlgChtr/pgps.m h u	  
         __sig__0 #  #  $  z	  
         __sig__1 %  t%  %  &
        *   /usr/local/magma-2.5/package/RngPol/misc.m   (
                                                                  (  (  (  
  )
  
         __sig__0   x    *
            (  (                +
        3   /usr/local/magma-2.5/package/Grp/is_conj_subgroup.m ,
        3   /usr/local/magma-2.5/package/Grp/is_conj_subgroup.m X-
        M   Whether a conjugate of N is a subgroup of M, and if so, a conjugating element   <  .
                                                              (  (  (    /
  
         __sig__0       0
            (  (              !  1
           IsConjugateSubgroup  #  #  2
                 (                              3
        +   The set of conjugates of H by elements of G &  '  	
           InternalFixSecondarySubmodule     

                 (                              
        1   /usr/local/magma-2.5/package/RngInvar/relations.m   0
        1   /usr/local/magma-2.5/package/RngInvar/relations.m   h0
            `(  l(                
        &   SquarefreePartialFractionDecomposition    
                 h(                              
        2   The (complete) partial fraction decomposition of f       
                         Q                                            (  `(  |(    "
            `(  (                 #
           PartialFractionDecomposition "  "  $
                 (                              %
        *   /usr/local/magma-2.5/package/RngPol/misc.m  0
           Centre ss p 	        ,   /usr/local/magma-2.5/package/RngInvar/prim.m 	        ,   /usr/local/magma-2.5/package/RngInvar/prim.m 	           __sig__0 variantsHard X5    	           Internal function        	                                                                     '  '  '      	            '  '                 	           InternalPrimaryInvariantsHard      	                 '                              	        +   /usr/local/magma-2.5/package/RngInvar/sec.m 0	        +   /usr/local/magma-2.5/package/RngInvar/sec.m x	                                                          a           P&  &  D&    	           SquareLatticeGraph  	  	  	                 H&                              	        B   The Paley graph of n; n must be a prime power congruent to 1 mod 4      	                                                          a           h&  &  \&  (  	  
         __sig__3   l    	            &  d&                	            &  &              $  	        :   Secondary invariants for invariant ring R using subgroup H  (	  @	  	                                                              (   (  '  '  D   
            '  '              d  
        )   Secondary invariants for invariant ring R   ,  D  
                                                                     (  '  (  x  
  
         __sig__1        
            '  (              0  
        	   relations rySubmodule     
  
         Internal   4  l  
                                                                    (  '  (  \"  
  
         __sig__2 #  d#  |#  
            '  (              $  
           __sig__0 &  @&  X&  p&  &  	  
      
   PaleyGraph  x    	                 `&                              	           The Clebsch graph       	                                                             a           &  &  t&  L#  	  
         __sig__4 $  $$  \$  	            &  |&              (&  @&  X&  	                                                             a           &  &  &    	  
         __sig__7 	  T	  l	  	            &  &              
  	        G   Display the Burnside matrix corresponding to the lattice of subgroups L T      	                                                               H'  8'  ('  ,'  d  	  ,         The i-th Steenrod operation P^i(f) of f (f must be a multivariate polynomial with coefficients in a finite field and i must be a non-negative integer)    	                                                                   x'  h'  l'  x  	            h'  t'                	           SteenrodOperation       	                 p'                              	        *   Return whether invariant ring R is modular  !  !  	                                                                     '  h'  '  $  	            h'  '              X&  	  
         GewirtzGraph   t  	                 &                              	           The Cayley graph of the group G       	                                                                   &  &  &    	  
         __sig__8   x    	            &  &              H  	  
         CayleyGraph     	                 &                              	        -   The Schreier graph for group G and subgroup H   \"  	                                                                &  &  &  %  	  
         __sig__9 &  &  &  	  
         SchreierGraph     	                 &                              	        (   /usr/local/magma-2.5/package/Sys/names.m 
  	        (   /usr/local/magma-2.5/package/Sys/names.m   8	           Assign Q to the names of S      	                                                            '  '  '    	  
         __sig__0   <  T  	            '  '                	           SysAssignNamesNum       	                 '                              	        1   /usr/local/magma-2.5/package/SubGrpLat/burnside.m   	        1   /usr/local/magma-2.5/package/SubGrpLat/burnside.m   8	  
         __sig__1 trix   $  	  
         __sig__0 %  p%  %  	            ('  4'              &  	  
      	   IsModular       	                 '                              	        &   A free resolution of (the module of) R  8
  	                                                                     '  h'  '     	  
         __sig__2       	            h'  '              @  	  
         __sig__0 ion      	        .   A minimal free resolution of (the module of) R    	                                                                     '  h'  '  |  	  
         __sig__3   0  H  	            h'  '                	           The homological dimension of R  !  	                                                                     '  h'  '  $  	  
         __sig__4 %  %  $&  	            h'  '              |'  	           DisplayBurnsideMatrix   `  	                 0'                              	        J   Display the Burnside matrix corresponding to the lattice of subgroups of G      	                                                               X'  P'  ('  D'  h  	  
         __sig__1   `    	            ('  L'              (  	        J   Display the Burnside matrix corresponding to the lattice of subgroups of G  t    	                                                                   `'  ('  T'  x  	  
         __sig__2   p    	            ('  \'              x!  	        ,   /usr/local/magma-2.5/package/RngInvar/misc.m 	     
   ,   /usr/local/magma-2.5/package/RngInvar/misc.m 	           __sig__0 &  &  &  &  '  O
            InternalSmallGroupProcessRestart   x    P
                 0)                              Q
  x        Returns a small group process. This will iterate through all groups with order in Orders. To extract the current group from a process, use ExtractGroup(). To move to the next group in a process, use NextGroup(). To find out which group the process currently points to, use ExtractLabel(). The user may limit the process to soluble or insoluble groups by setting Search. Search may take the values "All", "Soluble" or "Insoluble" (or variants thereof).     R
                                                               `)  P)  )  D)  x!  T
            )  L)              "  U
           SmallGroupProcess   #  $  V
                 H)                              Y
  
         __sig__3 '  <'  |'             domain  {   A
  
         CommutatorGroup    B
                 (                              C
        +   /usr/local/magma-2.5/package/Grp/smallgps.m 0hD
         +   /usr/local/magma-2.5/package/Grp/smallgps.m xhM
  
         __sig__1 Group    E
        7   Moves the small group process tuple p to its next group       F
                                                                   )  )  )  t  G
  
         __sig__0     <  H
            )  )              |  I
           InternalNextSmallGroup  x  J
                 )                              S
           __sig__2 pProcessRestart "  K
        :   Returns the small group process tuple p to its first group  $  $  L
                                                                  8)  )  ,)  t(  (  (  4
                                                                 (  (  (      5
  
         __sig__1          6
            (  (                 7
        +   The set of conjugates of H by elements of G      8
                                                             p  (  (  (      9
  
         __sig__2      1:
            (  (                 ;
        -   /usr/local/magma-2.5/package/Grp/commutator.m 0<
        -   /usr/local/magma-2.5/package/Grp/commutator.m 0=
        5   The commutator group [H, K] = <(h,k): h in H, k in K>      >
                                                                 )  (  (      ?
  
         __sig__0   @
            (  (                N
            )  4)                W
  *         Returns a small group process as described above. This will iterate through all groups (g) with order in Orders which satisfy Predicate(g).   4  X
                                                            p)  h)  )  \)    Z
            )  d)                [
  "      h   Returns a small group process as described above. This will iterate through all groups (g) with order o.   0  H  \
                                                                )  x)  )  l)    ]
  
         __sig__4 !  T!  |!  ^
            )  t)              "  _
  *         Returns a small group process as described above. This will iterate through all groups (g) of order o which satisfy Predicate(g).   '  '  ((  x(  
           SolvableRadical        
           DirectSumDecomposition     
           CartanSubalgebra      $  
           IsRestrictedLieAlgebra           
  
         SemiSimpleType  l  
  
      
   IsSolvable  |   }   ]              
  
         IsNilpotent      
  
      
   RootSystem  |   }              finite     
  
         KillingMatrix     
           y   z   {   |   }   ~                              
        ,   /usr/local/magma-2.5/package/AlgLie/cartan.m (
  
         __sig__1 gebra  $  
        F    True if a Lie algebra of characteristic p > 0 is a restricted algebra  T  
                                                                     *  *  *    
  
         __sig__0        
            *  *              l  
           IsRestrictedLieAlgebra  T*             F ngElement v
                                                             )  )  )  )    x
            )  )              	  y
  *         Returns the first group (g) with order in Orders which satisfies the predicate and the search condition specified by Search (see above).     0  z
                                                             )  )  )  )  t  {
  
      	   __sig__10     t  |
            )  )              \  }
  "      l   Returns the first group (g) of order o which satisfies the search condition specified by Search (see above).     ~
                                                                     *  )  )  "  
  
      	   __sig__11   #  #  
            )  )              H%  
                                                                  *  *  )  *  $)  k
  
         __sig__7        l
            )  )              P  m
           InternalExtractSmallGroup   	  	  n
                 )                              o
  $      r   Returns the label (s,n) of the small group process tuple p. This is the order and number of the current group of p  (  @  p
                                                                      )  )  )  t  q
  
         __sig__8       r
            )  )              ,  s
           InternalExtractSmallGroupLabel    t
                 )                              u
  B         Returns the first group (g) of order o which satisfies Predicate. The user may limit the the search to soluble or insoluble groups by setting the parameter Search. Search may take the values "All", "Soluble" or "Insoluble" (or variants).   (  `
                                                                 )  )  |)     a
  
         __sig__5          b
            )  )              $  w
           __sig__9 allGroupLabel y    c
        H   Returns true if the small group process tuple has passed its last group.         d
                                                                     )  )  )      e
  
         __sig__6      7f
            )  )                 
  `      c  Returns a list of all groups of order o. The user may limit the search to soluble or insoluble groups by setting the parameter Search. Search may take the value "All", "Soluble" or "Insoluble" (or variants thereof). Some orders will produce a very large list of groups -- in such cases a warning will be printed unless the user specifies Warning := false.     
  
      	   __sig__12   L  x  
            )  *                
  
         SmallGroups @  `  
                 *                              
        $   As above, but with a list of orders.   l  
                                                                 0*  (*  )  *  \"  
  
      	   __sig__13   d#  |#  
            )  $*              $  
                                                              @*  8*  )  ,*  (  g
            InternalSmallGroupProcessIsEmpty   t    h
                 )                              i
        <   Returns the current group of the small group process tuple p $  \$  j
                                                                    )  )  )  '  
        ,   /usr/local/magma-2.5/package/AlgLie/cartan.m 
  
         DerivedSeries      
           LowerCentralSeries       
           UpperCentralSeries  d5    
  
         LeviSubalgebra  }   
  
      
   NilRadical    H6  
         CorootSystem        
         Degrees           
         Integral             
      	   Dimension      ,             DualKillingForm @     D             MatrixGroup               
         Irreducible        
      	   OverGroup           
         MaxRootLength       
         RepPerm            
         RootInclusion      
  
         Reflections                 ReflectionMatrices         
         SimpleCoroots        
         SimpleMatrices       
         RootLengths    <             RootRestriction P     T    
         SimpleRoots         
         StandardGroup      W           Advance ns    
      	   SimpleRep      H       L   -   /usr/local/magma-2.5/package/GrpCox/Coxeter.m   
         __sig__0            
         StandardHom    *    
         StandardRoots   \1             Type        
           NonNilpotentElement      
                 +                              
        /   /usr/local/magma-2.5/package/AlgLie/semsimalg.m   
         __sig__1                   ,  0,                 Z                         8                                           p-  8-  d-    \            8-  l-              t  ]        9   The dimension of the n-th homology group of the complex C   <  \  ^                             8                                     -  8-  t-  H  _  
         __sig__3       `            8-  |-              8!  a           DimensionOfHomology "  "  b                 x-                              k  
         __sig__5 ogy %  %  c        F   The sequence of the dimensions of the homology groups of the complex C  T)             Pushout  on 
  
         AdjointMatrix      
                 4+                              
        *   Test whether the Lie algebra L is solvable  
  
  
                                                                     T+  *  H+  `  
  
         __sig__7   P  h  
            *  P+                
        +   Test whether the Lie algebra L is nilpotent <  T  
                                                                 +  d+  *  X+  ,  
  
         __sig__8       
            *  `+              h  
        ,   /usr/local/magma-2.5/package/AlgLie/nilrad.m 	
        ,   /usr/local/magma-2.5/package/AlgLie/nilrad.m 	
        $    The nilradical of the Lie algebra L %  %  
                                                                     |+  l+  p+  T)  
                 *                              
        *   The Cartan subalgebra of the Lie algebra L      
                                                                     *  *  *  "  
            *  *              #  
           CartanSubalgebra %  t%  %  
                 *                              
        ,   /usr/local/magma-2.5/package/AlgLie/center.m p
        ,   /usr/local/magma-2.5/package/AlgLie/center.m p
           The centre of the Lie algebra L l	  	  	  
                                                                     *  *  *    
  
         __sig__0   x    
            *  *                
        /   The centralizer of ideal K in the Lie algebra L (  H  t  
                                                                   *  *  *  <  
  
         __sig__1   ,  D  
            *  *              H  
        .   The normalizer of ideal K in the Lie algebra L     
                                                                   *  *  *  #  
  
         __sig__2 $  $  $  
            *  *              &  
        '   The derived series of the Lie algebra L $)  <)  T)  
  &      }   Returns a list of all groups (g) with order o which satisfy Predicate(g) eq true and the search condition specified by Search       
  
      	   __sig__14           
            )  4*                  
        $   As above, but with a list of orders.        
                                                                  H*  )  <*      
  
      	   __sig__15           
            )  D*                  
        ,   /usr/local/magma-2.5/package/AlgLie/attrib.m P
  
         __sig__0      d5
            l+  x+                 
  
      
   NilRadical  d5    
                 t+                              
        )    The soluble radical of the Lie algebra L     H6
                                                                     +  l+  +     
  
         __sig__1   d5    
            l+  +                
        -   /usr/local/magma-2.5/package/AlgLie/nonnilp.m 
        -   /usr/local/magma-2.5/package/AlgLie/nonnilp.m 
        8    True if the element x of the Lie algebra L is nilpotent   d5    
                                                                   +  +  +    
  
         __sig__0 d5       
            +  +              5
        ,   A non-nilpotent element of the Lie algebra L       
                                                                     +  +  +     
  
         __sig__1 
         
            +  +              0  =  
      
   Return v^n      >                                                                  -  ,  ,  p	  ?  
         __sig__6 
  
  
  @            ,  ,                A                             l    l                  l           -  ,        B  
         __sig__7       C            ,  -              x  D           ComponentProduct       E                 -                              F                            l                           l       h.   -  ,      l  G  
         __sig__8   $   l   H            ,  -              !  I        "   Return the minimal polynomial of v  #  #  J                                                                  0-  ,  $-  &  K  
         __sig__9 (  (  (  L            ,  ,-              +                   +                                      ,   /usr/local/magma-2.5/package/AlgLie/dirdec.m         ,   /usr/local/magma-2.5/package/AlgLie/dirdec.m         #   The matrix of the Killing form of L                                                                w           ,  ,  ,                  ,  ,                   
         KillingMatrix      	                 ,                                
         __sig__0 ition  (  
        E   A list of ideals of the Lie algebra L such that L is their direct sum                                                                          4,  ,  (,              
                                                                     +  *   +      
  
         __sig__3            
            *  +                  
        -   The lower central series of the Lie algebra L       
                                                                     +  *  +      
  
         __sig__4            
            *  +                  
        -   The upper central series of the Lie algebra L       
                                                                     ,+  *   +      
  
         __sig__5            
            *  (+                  
        F   The adjoint matrix corresponding to the element x of the Lie algebra L      
                                                                   <+  *  0+      
  
         __sig__6            
            *  8+                  M        -   /usr/local/magma-2.5/package/AlgBas/complex.m  %N     B   -   /usr/local/magma-2.5/package/AlgBas/complex.m  %O        W   Create the complex given by the list L of maps and such that the last term has degree d       P                                                        8          H-  8-  <-    Q  
         __sig__0   (    R            8-  D-                S  "      h   The homology group in degree n of the complex C as an A-module, together with the associated epimorphism       T                             8                                h-  X-  8-  L-     U  
         __sig__1 !   "  "  V            8-  T-              x#  W  
         Homology $  $  $  X                 P-                              Y        0   The sequence of homology groups of the complex C )  )  *  [  
         __sig__2 ,  8,  X,  ,                                                                    ,  ,        /  
         The basis of B  	  0                                                                    ,  ,  ,    1  
         __sig__3       2            ,  ,                3        2   The index positions of the projective modules of B      4                                                                    ,  ,  ,    5  
         __sig__4   \  |  6            ,  ,              x  7           IdempotentPositions     8                 ,                              9           Return whether v is a unit  #  #  :                                                                    ,  ,  ,  &  ;  
         __sig__5 (  (  (  <            ,  ,              +             CME  mology   
         SemiSimpleType                      l,                                       +   /usr/local/magma-2.5/package/AlgBas/stuff.m P),!        +   /usr/local/magma-2.5/package/AlgBas/stuff.m ),-  
         __sig__2 rators     "                                                                    ,  ,        #  
         __sig__0 t6       $            ,  ,              vl2%           IdempotentGenerators       &                 ,                              '                                                                    ,  ,         (  
         __sig__1   W3    )            ,  ,                *           NonIdempotentGenerators     +                 ,                              .            ,  ,                             SEA sitions 
        /   /usr/local/magma-2.5/package/AlgLie/semsimalg.m h0
             Create a classical Lie algebra          
                                                                +  +  +      
  
         __sig__0          
            +  +                 
           SimpleLieAlgebra      7
                 +                              
        *   /usr/local/magma-2.5/package/AlgLie/levi.m  p.h0
        *   /usr/local/magma-2.5/package/AlgLie/levi.m  .h0
        &   A Levi subalgebra of the Lie algebra L     
                                                                      +  +  +  )  
  
         __sig__0         
            +  +                             DirectSumDecomposition                      ,,                                      0   /usr/local/magma-2.5/package/AlgLie/rootsystem.m 
  p03        0   /usr/local/magma-2.5/package/AlgLie/rootsystem.m   03        +   The root system of a semisimple Lie algebra                                                                         H9  T,  D,  H,  T              D,  P,                  
      
   RootSystem  l                     L,                                      *   /usr/local/magma-2.5/package/AlgLie/type.m  X23        *   /usr/local/magma-2.5/package/AlgLie/type.m  23        $   The type of a semisimple Lie algebra #  $                                                                       t,  d,  h,  |'    
         __sig__0 )  <)  T)              d,  p,               ,              HasLeviSubalgebra   )  $)             __sig__0 *  @+  +  +  +  u        9   The quotient complex of C by the sequence S of submodules       v                           8                          8      /  -  8-  -  
  x            8-  -              @  y           The direct sum of C and D   x    z                         8   8                          8          -  8-  -    {  
         __sig__8     $  |            8-  -              t  }        <   Create the chain map from C to D all of whose terms are zero   |  ~                         8   8                          9           .  8-  -  h     
         __sig__9 !  !  !              8-  -              #    
         ZeroChainMap #  $                   -                                         The module maps of f '  '                           9                                           .  8-  .  ,  d                         8                                           -  8-  -    e  
         __sig__4 	  	  	  f            8-  -              (  g           DimensionsOfHomology   p  h                 -                              i        "   The subcomplex of C generated by S      j                           8                          8      /  -  8-  -    l            8-  -              <  m  
      
   Subcomplex  ,  D  n                 -                              o           The quotient complex of C by D     p                         8   8                          8      -  -  8-  -  #  q  
         __sig__6 $  $  $  r            8-  -              &  s  
         QuotientComplex '  t                 -                              w           __sig__7 ,  ,  ,  -  \-                           8                                8           /  8-  /      B         Given a complex C of modules over a basic algebra, return the complex of lenth one greater that is obtained by adding the quotient map to the homology module from the term of lowest degree in the complex on the right end of the complex.       
      	   __sig__28   ,                8-  \/                           RightExactExtension                       X/                                P      &  Given a complex C of modules over a basic algebra, return the complex of lenth two greater that is obtained by adding the inclusion from the homology to the term of highest degree in the complex and also appending the quotient map from the homology to the term of highest degree in the complex.  &                           8                                8          x/  8-  l/  +    
      	   __sig__29   -  `-  X                
      	   __sig__10                   8-  .                  
      
   ModuleMaps    	                   .                                         The kernel complex of f D  \  t                           9                                8          0.  8-  $.      
      	   __sig__11                   8-  ,.              (             The kernel complex of f x                               9                                8          @.  8-  4.      
      	   __sig__12   4  l              8-  <.                            The image complex of f  "                           9                                8      xJ  P.  8-  D.  L%    
      	   __sig__13   p&  &              8-  L.              x(          %   The sum of the two chain maps f and g   +       &   .   /usr/local/magma-2.5/package/AlgBas/algebras.m P                                                          w           /  /      d5  
         __sig__0                     /  /                    
         MapToMatrix                         /                                
         __sig__2 gBas                 The Jacobson radical of M d5                                                                          /  /  /  d5  
         __sig__1                     /  /                    0         Returns true if the module is projective and returns a list of how many projective modules of each type are direct summands of the projective cover of the module.  
  
    
         __sig__6                   /  D0              0    .         Returns true if the module is injective and returns a list of how many injective modules of each type are direct summands of the injective hull of the module.  t                                                                       X0  /  L0  D    
         __sig__7                   /  T0                  &      ~   Returns the pushout of the diagram [ M1 <-- fc1 -- D --- fc2 --> M1 ] as an AModule together with homomorphisms from M1 and M2  $                              w       w            w w           h0  /  \0  |'    
         __sig__8 )  <)  T)              /  d0               ,                   `0                              ]           Current ors             /  0              6  `      `  Given an sequence X of elements in a module over a basic algebra and a sequence N of nonnegative integers, the function creates the homomorphism from the projective module that is a direct sum of N[i] copies of the ith projective module for the algebra to the module of X with the property that the idempotent e of the projective module maps to X[i]*e.                                                                  w            0  /  0      
         __sig__4                     /  0                  	  ^      ]  The projective cover of M given as the projective module P, the surjective homomorphism of P onto M, the sequences of inclusion and projection homomorphism of P from and to its indecomposable direct summands and the isomorphism type of P in the form of a list of the number of copies of the projective modules of algebra of each type that make up P.    3
                                                         w              00  /  $0       
         __sig__5   4                /  ,0                  
         ProjectiveCover                     (0                                                                                                   H0  /  <0                quot  m m              LeftZeroExtension                         .                                8         Given a complex C of modules over a basic algebra, return the complex of lenth one greater that is obtained by adding the zero map to the zero module from the term of lowest degree in the complex.                              8                                8          /  8-  .  $    
      	   __sig__24                   8-  /              <             RightZeroExtension  \  |                    /                                P      &  Given a complex C of modules over a basic algebra, return the complex of lenth two greater that is obtained by adding the zero map to the zero module from the term of lowest degree in the complex and also appending the zero map from the zero module to the term of highest degree in the complex.  )    
      	   __sig__25    ,   ,              8-  /              -  .  .                           9   9                          9      dn  `.  8-  T.        
      	   __sig__14                       8-  \.                          /   The product of the scalar s and the chain map f                                      9                              9      x.  p.  8-  d.        
      	   __sig__15                       8-  l.                          -   The composition of the two chain maps f and g                                9   9                          9      E  .  8-  t.        
      	   __sig__16                       8-  |.                          0   True iff the chain map f is zero in every degree                                     9                                           .  8-  .        
      	   __sig__17                       8-  .                          8   True iff the chain map f is an injection in every degree                                     9                                       P0  .  8-  .        
      	   __sig__18                       8-  .                          8   True iff the chain map f is a surjection in every degree                                     9                                       H  .  8-  .        
      	   __sig__19                       8-  .                          :   True iff the chain map f is an isomorphism in every degree                                   9                                       H  .  8-  .        
      	   __sig__20                       8-  .                    *         The dual of the complex C as a complex over the opposite algebra of the algebra of C. The last term of the dual complex is in degree 0.                                      8                                8      .  .  8-  .        
      	   __sig__21                       8-  .                    *         The dual of the complex C as a complex over the opposite algebra of the algebra of C. The last term of the dual complex is in degree n.                                          8                          8      3  .  8-  .        
      	   __sig__22                       8-  .                    8         Given a complex C of modules over a basic algebra, return the complex of lenth one greater that is obtained by adding the zero map from the zero module to the term of highest degree in the complex.                                8                                8          .  8-  .        
      	   __sig__23                       8-  .                              8-  t/                   
         ExactExtension                     p/                                
      	   __sig__31 gy 
  
                               9                          u           /  8-          
      	   __sig__30                   8-  /                           InducedMapOnHomology                      /                                N        The subcomplex generated by L. The list L may be either a list of sequences of element of the terms of C or a list of submodules of the terms of C. There must be one element of L for each term of C. The function returns both the subcomplex and the inclusion of the subcomplex into C. #  $                               8                          89          /  8-  /  |'              8-  /              )                               8                          89          /  8-  /  /  $/  L/    
         ZeroExtension                       /                                      -   Returns the list of the terms of the complex.   
                           8                                8          8/  8-  ,/  `    
      	   __sig__26   P  h              8-  4/                  @         Given a complex C of modules over a basic algebra, return the complex of lenth one greater that is obtained by adding the inclusion map from the homology to the term of highest degree in the complex to the left end of the complex.                             8                                8          H/  8-  </  "    
      	   __sig__27   0#  H#              8-  D/              $             LeftExactExtension  <&  T&                   @/                                                       8                                8          `/  8-  T/  -  <            /  0              $  =           DimensionsOfProjectiveModules     >                 0                              ?        Q   The sequence of the dimensions of the injective modules of the basic algebra $A$.     4  @                                                                    1  /  0    A  
      	   __sig__15   L  x  B            /  1                C           DimensionsOfInjectiveModules   @  D                  1                              E  V      7  True if the module M is a semisimple module and false otherwise. If true, then the function also returns a list of the ranks of the primitive idempotents of the algebra. This is also a list of the multiplicities of the simple modules of the algebra as composition factors in a composition series for the module. x(  (  (  F                                                                      1  /  1  -  H            /  1              /             JacobsonRadicalAlgBas                       /                                >         Given an element x in a module over a basic algebra, creates the homomorphism from the nth projective module for the algebra to the module with the property that the idempotent e of the projective module maps to x*e   (  @                                                         w       0  /  /  /  t              /  /              \             LiftHomomorphism   t                      /                                N        Given a sequence S = [s_1,s_2, ... ], the function returns a projective module which is the direct sum of s_1 copies of the first projective of the algebra A, s_2 copies of the second, etc. It also returns the sequences of inclusions and projections onto the incecomposable projecitves.  (                                                                     0  /  0  -             __sig__3 /  d/  |/  /  /    P         The quotient of C by the subcomplex generated by L. The list L may be either a list of sequences of element of the terms of C or a list of submodules of the terms of C. There must be one element of L for each term of C. The function returns both the quotient complex and the quotient map.              
      	   __sig__32                       8-  /                          .   /usr/local/magma-2.5/package/AlgBas/algebras.m P          Given a module M over a basic algebra and a natural number n the function computes a projective resolution for M out to n steps. The function returns the resolution in compact form together with the augmentation map (P_0 -> M). The compact form of the resolution is a list of the the minimal pieces of information needed to reconstruct the boundary maps in the resolution. That is the boundary map (P_{i+1} -> P_i) is recorded as a tuple consisting of a matrix whose entries are the images of the generators for indecomposable projective modules making up P_{i+1} in the indecomposable projective modules making up P_i and two lists of integers givin the number of indecomposable projective modules of each isomorphism class in P_{i+1} and in P_i. 4#  L#                                                                    82  1  ,2  &    
         __sig__2 '  '  '              1  42              *             CompactProjectiveResolution ,  ,                   02                                
         __sig__3 0  0  1             ZeroMap  on   
         __sig__0   L  d              1  2                           SimpleHomologyDimensions 	  	  	                    2                                ,         The sequence of sequences of dimensions of the cohomology groups Ext^j(Si,M) for simple modules Si, to the extent that they have been computed.                                                                            2  1  2      
         __sig__1                   1  2                            SimpleCohomologyDimensions                       2                                               H2                                F         The complex giving the minimal projective resolution of M together with the augmentation homomorphism from the projective cover of M into M. Note that homomorphisms go from left to right so that the cokernel of the last homomorphism in the complex is M.    .    
         __sig__4 /  /   0              1  d2              1  1  1  o           CohomologyRightModuleGenerators     p                 1                              q  R      )  Given projective resolutions P and Q for simple module S and T over a basic algebra A and the cohomology generators for T associated to the resolution Q, the function returns the chain maps of the minimal generators for the cohomology Ext*(S,T) as a left module over the cohomology ring Ext*(S,S).   (      r                                                                 1  x1  1     s  
         __sig__3 +         t            x1  1              +  u           CohomologyLeftModuleGenerators  ,  v                 1                              w        I   Returns the degrees of the chain maps of the generators of the cohomology          y  
         __sig__4            !  
         Pullback       "                 x0                              #  $      r   The nth irreducible module of the algebra. The module is the quotient of the nth projective module by its radical.  X  p  $                                                                 0  /  0    %  
      	   __sig__10       &            /  0              $  '           IrreducibleModule   ,  t  (                 0                              )  $      r   The nth irreducible module of the algebra. The module is the quotient of the nth projective module by its radical.        *                                                                 0  /  0  #  +  
      	   __sig__11    %  H%  ,            /  0              &  -  
         SimpleModule (  t(  .                 0                              5  
      	   __sig__13 ion   \-  1  
      	   __sig__12   $/  L/  \           Dual odule    &      }   Returns the pullback of the diagram [ M1 -- fc1 --> N <-- fc2 -- M2 ] as an AModule together with homomorphisms to M1 and M2.                                   w       w            w w        K  0  /  t0        
         __sig__9                         /  |0                  I        <   Returns the identity (n x n)-matrix over the finite field F.     J                             q                           w           01  /  $1  
  K  
      	   __sig__17       L            /  ,1              0  M  
         IdentityMatrix  0  N                 (1                              a  
         __sig__0 ism   t  O        @   True if the map f is a homomorphism of modules over the algebra.   t    P                         w                                 
           H1  /  <1  x  Q  
      	   __sig__18   p    R            /  D1              x!  S           IsModuleHomomorphism "  "  T                 @1                              U        *   /usr/local/magma-2.5/package/AlgBas/attr.m  V        .   /usr/local/magma-2.5/package/AlgBas/chainmap.m W           OppositeAlgebra X,  x,  ,  Y           CompactProjectiveResolution $/  L/  g           __sig__1 erators 0  0  0  /  6         If $v$ is an element of a basic algebra given as a vector in the underlying space, then the function computes the matrix of the action by right multiplication of the element on the algebra.     0                                                                    0  /  0  h  2            /  0                3  "      n   Tht algebra $A$ as a right module over itself. The module is the direct sum of the projectives modules of $A$.  \  4                                                                   0  /  0  H  6            /  0                7           RightRegularModule  P!  x!  8                 0                              G        	   __sig__16 iveModules    $  9        R   The sequence of the dimensions of the projective modules of the basic algebra $A$.  (  (  :                                                                    0  /  0  -  ;  
      	   __sig__14   d/  |/  Z                    k  R      *  Given projective resolutions P and Q for simple module S and T over a basic algebra A and the cohomology generators for T associated to the resolution Q, the function returns the chain maps of the minimal generators for the cohomology Ext*(S,T) as a right module over the cohomology ring Ext*(T,T).  P  h  l                                                                 1  x1  1    n            x1  1                x                                                                     1  x1  1    z            x1  1                {           DegreesOfCohomologyGenerators      |                 1                              }        -   /usr/local/magma-2.5/package/AlgBas/compact.m x~        -   /usr/local/magma-2.5/package/AlgBas/compact.m x        M   The sequence of sequences of dimensions of the homology groups been computed.    ,                                                                      2  1  1  l0  	           Rank 1  L1  [           CompactInjectiveResolution  x    ^     
   .   /usr/local/magma-2.5/package/AlgBas/chainmap.m ؖ_  2         Given a projective resolutions P for a simple module S over a basic algebra A, the function returns the chain maps of the minimal generators for the cohomology Ext*(S,S).      `                                                                     1  x1  |1  $  b            x1  1              t          y  Given a module M over a basic algebra and a natural number n the function computes an injective resolution for M out to n steps. The function returns the resolution in compact form together with the coaugmentation map (M -> I_0). The compact form of the resolution is a list of the the minimal pieces of information needed to reconstruct the boundary maps in the resolution. That is the boundary map (I_i -> I_{i-1}) is recorded as a tuple consisting of a matrix whose entries are the images of the generators for indecomposable injective modules making up I_i in the indecomposable injective modules making up I_{i-1} and two lists of integers givin the number of indecomposable projective modules of each isomorphism class in I_i and in I_{i-1}. The actual return of the function is the compact projective resolution of the dual module of M over the opposite algebra of the algebra of M.   '  '                                                                    P2  1  D2  ,              1  L2              P/             CompactInjectiveResolution  0  1  c           CohomologyRingGenerators   x    d                 1                              e  "      g   Given the generators for cohomolgy, the function returns the list of degrees of the minimal generators. "  "  "  f                                                                     1  x1  1  (&  h            x1  1              '  i           DegreesOfGenerators )  )  j                 1                                         __sig__5 ion ution  s   P/  m  
         __sig__2 0  0  0                                                                   2  1  2      
         __sig__6 	  T	  l	              1  2              
    
         __sig__2 bra        $      r   The nth injective-syzygy module of M. The cokernel of the nth boundary map in a minimal injective resolution of M.                                                                       2  1  2      
         __sig__7   t                1  2              D             InjectiveSyzygyModule   H                   2                                      .   /usr/local/magma-2.5/package/AlgBas/creation.m ȟ        .   /usr/local/magma-2.5/package/AlgBas/creation.m ȟ  &      {   Given a finite p-group G and a field k of characteristic p and returns the group algebra kG in the form of a basic algebra. *  *                           q                                     2  2  2  2  |/    
         __sig__0 0  0  0              2  2              <2  T2  l2    N        Given a finite permutation group G, with normal subgroups N and M, such that N < M and M/N is soluble, if M/N has a complement in G/N return a list of representatives of the conjugacy classes of M/N in G/N. If M/N does not have a complement in G/N, the empty sequence is returned                   3  4              D          5   /usr/local/magma-2.5/package/GrpPerm/complement_new.m p	        5   /usr/local/magma-2.5/package/GrpPerm/complement_new.m p
  F         Given a finite permutation group G, with normal subgroup M such that M is soluble, if M has a complement in G return a list of representatives of the conjugacy classes of M in G. If M does not have a complement in G, the empty sequence is returned #  #  #                                                                     44  $4  (4   '    
         __sig__0 (  )  ()              $4  04              +    
         ComplementsNew  `-                   ,4                                
         __sig__1 1  81  P1              $4  H4              2  2  2             pGroupToBasicAlgebra                      2                                &      {   Given a finite p-group G and a field k of characteristic p and returns the group algebra kG in the form of a basic algebra. |                             q                                         2  2  2      
         __sig__1     (              2  2              x    ~        Creates a basic algebra from a minimal set of relations. The input is a free algebra, the number of idempotents, a list of the right and left idempotents corresponding to the nonidempotent generators of the algebra and a list of relations. The function creates the extra relations that are natural to the idempotents and the multiplications of the idempotents on the nonidempotent generators. Thus the user needs only supply the relations among the nonidempotent generators.  +  +                                       :                         2  2  2   0              2  2              1  8           MEANS ew 2                                                         8w           h2  1  \2               ProjectiveResolution                      `2                                D         The complex giving the minimal injective resolution of M together with the inclusion homomorphism from M into its injective hull. Note that homomorphisms go from left to right so that the kernel of the first homomorphism in the complex is M.    "  "                                                         8w           2  1  t2  H%              1  |2              &             InjectiveResolution (  (                   x2                                "      g   The nth syzygy module of M. The kernel of the nth boundary map in a minimal projective resolution of M. 1  41  L1    
      
   ZeroModule                       3                                         The zero map from M to N 	  	  	                                                        w           03  2  $3      
         __sig__5                   2  ,3                                 (3                                      +   /usr/local/magma-2.5/package/AlgBas/opalg.m          +   /usr/local/magma-2.5/package/AlgBas/opalg.m H  
         __sig__1 ule                                      >                               L3  @3      8!    
         __sig__0 "  0"  X"              @3  H3              #    ,         Given a basic algebra A, creates the opposite algebra. This is the algebra with the same set of elements but with multiplication * given by x*y = yx.   *              @3  `3              ,    
         OppositeAlgebra .                   \3                                
         __sig__2 1  1  2             OverN   2             MakeBasicAlgebra      Zz2                 2                                      0   Creates the tensor product of two basic algebras   Bz2                                                                    3  2  2      
         __sig__3 z2                   2  3              If3           The zero A-module                                                                             3  2  3      
         __sig__4                     2  3                    <         Given a basic algebra A and its opposite algebra O, creates the change of basis matrix B from the vector space of A to the vector space of O, so that if x, y are in A then (xy)B is the same as (yB)(xB) in O.   ,  D                                                           w           |3  @3  p3                @3  x3                           BaseChangeMatrix     (                   t3                                &      x   Returns the dual of a module M over a basic algebra A as a module over the algebra O which is the opposite algebra of A.                                                                      3  3  @3  3  "    
         __sig__3 #  #  #              @3  3              %    .         Given a homomorphism between two modules over a basic algebra A, returns the dual homomorphism between the dual modules over the opposite algebra O of A.   -  `-                           w                                 w           3  @3  3  P1    
         __sig__4 2  X2  p2    *         Given a finite permutation group G, with normal subgroup M such that M is soluble, if M has a complement in G return true, otherwise false.                                                                           L4  $4  @4                                                                         6  t6  x6                t6  6              	          %   InternalTransitiveGroupProcessIsEmpty                      |6                                      >    Moves the transitive group process tuple p to its next group                                                                       6  t6  6      
         __sig__1   @  `              t6  6                           InternalNextTransitiveGroup 4  L                   6                                       `   Returns a transitive group process. This will iterate through all groups with degree in Degrees. #  #  $                                                                 6  6  t6  6  '    
         __sig__2 )  @)  X)              t6  6              $,             TransitiveGroupProcess  -                   6                                                                                          6  6  t6  6  3  "            TwoTransitiveGroupIdentification      If3#                 |4                              $        /   /usr/local/magma-2.5/package/GrpPerm/oldtonew.m H%        /   /usr/local/magma-2.5/package/GrpPerm/oldtonew.m H&        9   Convert an old-style perm group to a new-style perm group   4      '                                                                     4  4  4     )            4  4              ow5*  
         OldToNew         +                 4                              ,        9   Convert an new-style perm group to a old-style perm group        -                                                                     4  4  4      .  
         __sig__1      z1/            4  4                 0  
         NewToOld   ~92    1                 4                              2        ,   /usr/local/magma-2.5/package/GrpPerm/pcore.m H3        ,   /usr/local/magma-2.5/package/GrpPerm/pcore.m H4  "      l   A minimal elementary abelian normal subgroup of G that lies in the elementary abelian normal subgroup N of G    )  5                                                                   4  4  4      6  
         __sig__0    +      7            4  4                 9                 4                              H           __sig__3 nNormalSubgroup    :        C   An elementary abelian normal subgroup of G, non-trivial if possible        ;                                                                     4  4  4  <3  <  
         __sig__1         =            4  4                                   3                                      1   /usr/local/magma-2.5/package/GrpPerm/complement.m            1   /usr/local/magma-2.5/package/GrpPerm/complement.m      F         Given a finite permutation group G, with normal subgroup M such that M is soluble, if M has a complement in G return a list of representatives of the conjugacy classes of M in G. If M does not have a complement in G, the empty sequence is returned                                                                       4  3  3  3      
         __sig__0                   3  3                    *         Given a finite permutation group G, with normal subgroup M such that M is soluble, if M has a complement in G return true, otherwise false. %  (&                                                                     4  3   4  *    
         __sig__1 ,  <,  \,              3  4               .                                                                   4  3  4  2             __sig__2 2   3  83  T3  l3             PathTreeCyclicModule                       D3                                                                                                 d3  @3  X3                          @3  3                         -   The injective hull of the nth simple A-module                                                                  3  3  @3  3      
         __sig__5                   @3  3                  
         InjectiveModule                    3                                0         The injective module that is the injective hull of direct sum of S[1] copies of the first simple module for the algebra, S[2] copies of the second simple module, etc.                                                                     3  @3  3  x!    
         __sig__6 "  "  "              @3  3              #    *         Given a module M over a basic algebra A, returns the injective hull I of M as an A-module and the inclusion homomorphism theta: M --> I. )  )  *                                                           w  w w           3  @3  3  L/    
         __sig__7 0  0  0              @3  3              2          %   As above, but with a list of degrees.                                                                      7  t6  7  <
    
      	   __sig__14   L  d              t6  7                  
         __sig__0 scription          G   Return the string description of the n-th transitive group of degree d.                                                                          7  t6  7      
      	   __sig__15                   t6  7                            TransitiveGroupDescription                       7                                      0   /usr/local/magma-2.5/package/GrpPerm/Aut/autgp.m #  00        0   /usr/local/magma-2.5/package/GrpPerm/Aut/autgp.m &  0        2   Automorphism group of a finite permutation group G  @)  X)                                                            "             7  7  7   .              7  7              p0          4   /usr/local/magma-2.5/package/GrpPerm/Aut/backtrack.m 0  
         CartanMatrix 3  <4    
         InjectiveHull   3             HasComplementNew                         D4                                N        Given a finite permutation group G, with normal subgroups N and M, such that N < M and M/N is soluble, if M/N has a complement in G/N return a list of representatives of the conjugacy classes of M/N in G/N. If M/N does not have a complement in G/N, the empty sequence is returned (  H  t                                                                   d4  $4  X4  <    
         __sig__2   ,  D              $4  `4              H    
         ComplementNew                      \4                                      /   /usr/local/magma-2.5/package/GrpPerm/dtgroups.m  }                                                              6  5  45  5                45  5              	          (   Returns the first group (g) of degree d.                                                                             6  45   6  h    
      	   __sig__10   `                45  6              (    :         Returns a sequence of all primitive groups of degree d. Some degrees will produce a very large sequence of groups -- in such cases a warning will be printed unless the user specifies Warning := false.                                                                        ,6  6  45  6  "    
      	   __sig__11   #  #              45  6              H%    
         PrimitiveGroups &                   6                                      %   As above, but with a list of degrees.   X,                                                                  <6  46  45  (6  0    
      	   __sig__12   1  1              45  06              43    
      	   __sig__13   4  4             N         \  
         __sig__2        ]            45  p5              P  ^           PrimitiveGroupProcess   l	  _                 l5                              `  &      ~   Returns a primitive group process which will iterate through all groups (g) with degree in Degrees which satisfy Predicate(g).  @  a                                                            5  5  45  5  t  b  
         __sig__3       c            45  5              ,  d        T   Returns a primitive group process. This will iterate through all groups of degree d.     e                                                                5  5  45  5  #  f  
         __sig__4 #  #  $  g            45  5              %  h  $      o   Returns a primitive group process. This will iterate through all groups of degree d which satisfy Predicate(g). +   ,   ,  i                                                                 5  45  5  l0  j  
         __sig__5 1  1  1  k            45  5              2  n  
         __sig__6 4  P4  h4             hook x up   O                                                                     D5  45  85      Q            45  @5                 R        $   InternalPrimitiveGroupProcessIsEmpty (      S                 <5                              T        =    Moves the primitive group process tuple p to its next group    Kӽ5U                                                                  \5  45  P5     V  
         __sig__1   )c6    W            45  X5                X           InternalNextPrimitiveGroup       Y                 T5                              Z         _   Returns a primitive group process. This will iterate through all groups with degree in Degrees.  4         [                                                               5  t5  45  h5              /   /usr/local/magma-2.5/package/GrpPerm/dtgroups.m h(           __sig__0 pIdentification            %    Identify a doubly-transitive group g                                                                            4  t4  x4        
         __sig__0 4         !            t4  4                  l        B    Returns the current group of the primitive group process tuple p     P  m                                                                      5  45  5  (  o            45  5              p  p           InternalExtractPrimitiveGroup     q                 5                              r  &      y    Returns the label (s,n) of the primitive group process tuple p. This is the degree and number of the current group of p    t    s                                                                      5  45  5  x  t  
         __sig__7   p    u            45  5              x!  v        "   InternalExtractPrimitiveGroupLabel  0#  H#  w                 5                              x        B   Returns the first group (g) of degree d which satisfies Predicate.  (  (  y                                                               5  5  45  5  -  {            45  5              /  |        Q   Returns the first group (g) with degree in Degrees which satisfies the predicate.   3  43  ~  
         __sig__9 4  4  4  >           ElementaryAbelianNormalSubgroup d  ?                 4                              @        E   An elementary abelian normal p-subgroup of G, non-trivial if possible     A                                                                   5  4   5  4  B  
         __sig__2   ,  D  C            4  5                D            pElementaryAbelianNormalSubgroup       E                 5                              F        6   Compute pCore(G, p) using the algorithm of Bill Kantor  L  G                                                                   $5  4  5  !  I            4   5              #  J  
         pCoreKantor #  $  K                 5                              L        -   /usr/local/magma-2.5/package/GrpPerm/prmgps.m  M         -   /usr/local/magma-2.5/package/GrpPerm/prmgps.m  z  
         __sig__8 imitiveGrouN        H    Returns true if the primitive group process has passed its last group.  2  X2  p2  P  
         __sig__0 3  3  3          /   /usr/local/magma-2.5/package/GrpPerm/Aut/comp.m         4   /usr/local/magma-2.5/package/GrpPerm/Aut/extendaut.m         1   /usr/local/magma-2.5/package/GrpPerm/Aut/oddfns.m .m        4   /usr/local/magma-2.5/package/GrpPerm/Aut/utilities.m         2   /usr/local/magma-2.5/package/GrpPerm/Aut/radquot.m m8        7   /usr/local/magma-2.5/package/GrpPerm/Aut/refineseries.m         3   /usr/local/magma-2.5/package/GrpCox/CoxAttributes.m         -   /usr/local/magma-2.5/package/GrpCox/Coxeter.m xP ʸ  
         codomain          
         __sig__0 sm finite    
         isomorphism         
         closure             
         regular d     l          
   surjective _finite                   generically_finite               	                                
         algebra_map                   C  C              ``ʸ  
         dominant                                                                                                                                                                                                                                                          Z   U   U                    1      C  C  C      l                           \   V   V                    2      C  C  C      t*    
         __sig__1 *     *              C  C              p1          7   Restrict the map f of ambient schemes to a map S - -> T 8     8                           [   V   U                    3      C  C  C  C  L8    
         __sig__2 8     C    "                                                                                                        $   The Cartan matrix of a Coxeter group                                ;                                       8  p8  `8  d8  1            `8  l8                   
         CartanMatrix 7                     h8                                      *   The Cartan matrix of a given type and rank    vl2                                                                8  8  `8  |8     !  
         __sig__1   Ҏ5    "            `8  8                #        3   The Cartan matrix of a given compound type and rank        $                                                                    8  `8  8  h+  %  
         __sig__2         &            `8  8                  '  &      y   The list consists of pairs describing the irreducible Cartan types; type X is returned for a component which is not valid     j7(                                                                 8  8  `8  8     )  
         __sig__3   i7    *            `8  8                +  
      
   CartanType 7       ,                 8                              -        <   A list of pairs describing the irreducible Cartan types of W                         6                                &      z    Returns the label (s,n) of the transitive group process tuple p. This is the degree and number of the current group of p   x                                                                          7  t6  7  0              t6  7                        #   InternalExtractTransitiveGroupLabel                      7                                &      y   Returns the first group (g) of degree d which satisfies Predicate, along with a string giving a description of the group.                                                                      47  ,7  t6   7  "              t6  (7              #    *         Returns the first group (g) with degree in Degrees which satisfies the predicate, along with a string giving a description of the group. )  )  *                                                                D7  <7  t6  07  L/    
         __sig__9 0  0  0              t6  87              2           _   Returns the first group (g) of degree d, along with a string giving a description of the group. 5   6  h6          R   Returns a list of all groups (g) with degree d which satisfy Predicate(g) eq true.                                                                    L6  D6  45  86                45  @6                         %   As above, but with a list of degrees.                                                                      T6  45  H6  $    
      	   __sig__14                   45  P6              <    
         __sig__0 cription           F   Return the string description of the n-th primitive group of degree d.                                                                       d6  45  X6  #    
      	   __sig__15   #  $              45  `6              %             PrimitiveGroupDescription   <'  |'                   \6                                      -   /usr/local/magma-2.5/package/GrpPerm/trngps.m          -   /usr/local/magma-2.5/package/GrpPerm/trngps.m   
         __sig__8 ansitiveGro        I    Returns true if the transitive group process has passed its last group.    5  5                                                                        L7  t6  @7      
      	   __sig__10   T	  l	              t6  H7              
    :         Returns a sequence of all transitive groups of degree d. Some degrees will produce a very large sequence of groups -- in such cases a warning will be printed unless the user specifies Warning := false.   H  t                                                                   l7  \7  t6  P7  <    
      	   __sig__11   ,  D              t6  X7              H             TransitiveGroups   p                     T7                                      %   As above, but with a list of degrees.   #                                                                  |7  t7  t6  h7  &    
      	   __sig__12   (  (              t6  p7              +          R   Returns a list of all groups (g) with degree d which satisfy Predicate(g) eq true.  /  /                                                                7  7  t6  x7  43    
      	   __sig__13   4  4              t6  7              h6    (         Returns a transitive group process which will iterate through all groups (g) with degree in Degrees which satisfy Predicate(g). 	  	  8
    
         __sig__3   H  `              t6  6                        U   Returns a transitive group process. This will iterate through all groups of degree d.                                                                     6  6  t6  6      
         __sig__4   <  \              t6  6                  $      p   Returns a transitive group process. This will iterate through all groups of degree d which satisfy Predicate(g).    !  8!                                                                   6  t6  6  $    
         __sig__5 %  p%  %              t6  6              &          C    Returns the current group of the transitive group process tuple p  +  +                                                                        6  t6  6  /    
         __sig__6 1  41  L1              t6  6              2             InternalExtractTransitiveGroup  4    
         __sig__7 5  5  5  V                         ;                                0           `9  `8  T9    X            `8  \9              	  Y        )   True if W is an irreducible Coxeter group       Z                         ;                                       ,b  p9  `8  d9  l  \            `8  l9                ]  &      |   Converts a sequence w of integers representing simple reflections to a permutation of the root system of the over group of W   @  ^                             ;                                     9  `8  t9    _  
      	   __sig__14       `            `8  |9              !  a  
      
   WordToPerm  "  "  b                 x9                              c  .         Convert a permutation p representing an element of W to a sequence of integers representing it as a word in the simple reflections of the over group of W   <,  \,  d                             ;                                     9  `8  9  0  e  
      	   __sig__15   1  1  f            `8  9              83  g  
      
   PermToWord  4  4  h                 9                              .                         ;                                           8  `8  8    /  
         __sig__4 	  T	  l	  0            `8  8              
  1        2   The string name of the type of the Cartan matrix C       2                                                                 8  8  `8  8    3  
         __sig__5     (  4            `8  8              t  5  
      
   CartanName      6                 8                              7            The string name of the type of W       8                         ;                                           8  `8  8  "  9  
         __sig__6 #  0#  H#  :            `8  8              $  ;           Print the Dynkin diagram of W   &  <                        ;                                      9  8  `8  8  +  =  
         __sig__7 ,  ,  ,  >            `8  8              L/  ?  
         DynkinDiagram   0  @                 8                              A        -   Print the Dynkin diagram of the Cartan matrix   4  C  
         __sig__8 5   6  h6  &                             V    V                  V           @  P@  @    '  
         __sig__3 	  X	  p	  (            P@  @              
  )           TrapezoidalQuadrature   D  *                 @                              +           The Beta function B(z, w)   ,  D  ,                         V    V                           V           @  P@  @  x  .            P@  @              `  /  
         BetaFunction   0  0                 @                              V        *   /usr/local/magma-2.5/package/RngLoc/misc.m  1     <   -   /usr/local/magma-2.5/package/AlgGeom/specfile   |#  5  
         __sig__0 2.5/packageW     6   *   /usr/local/magma-2.5/package/RngLoc/misc.m m`  
         __sig__0 2.5/package           faces      p            E  E              /sch_map.m  2        3   /usr/local/magma-2.5/package/AlgGeom/map/equality.m 8 !3        3   /usr/local/magma-2.5/package/AlgGeom/map/equality.m  !4                         Y   Y                                 @  @  @      7  6            @  @              9  7  
      
   SameDomain  :  :  8                 @                                      &            ;  <                '  
         RootFunction     (                 <                              )  6         Two sequences of matrices. The first represent the fundamental roots, the second represent the negatives of the fundamental roots for the simple Lie algebra of the given type and rank       *                                                          ;          <  ;  <  x  +  
      	   __sig__11     @  ,            ;  <                -  
         LieRoots   4  L  .                 <                              /  &      x   Returns the groups B, N and H giving the BN-pair for the Chevalley group of the given type and rank over the given field $  $  $  0                                                      j j j           <  ;  <  (  1  
      	   __sig__12   *  *  2            ;  <              ,  3  
         BruhatChevalley /  4                 <                              5        3   The degree of the representation with weight lambda T3  l3  6                         u    ;                                     <  ;  <  d7  7  
      	   __sig__13   9  9  8            ;  <              :  9  
      
   WeylDegree  ;   <    *         List of triples giving the position and value of the non-zero entries in the matrix for the adjoint action of e_alpha (acting on the right) )c6                             u    ;                                     p<  ;  d<                ;  l<                    
         AdjointEntries  7                 h<                                         Reverse the indexed set X 7                                 0                                 0           <  ;  |<  d5!  
         __sig__9       7  "            ;  <                  #        J   Given a nilpotent matrix mm, return the exponential function t -> exp(t*E)       $                                                          X           <  ;  <      %        	   __sig__10                   B                                                                   9  `8  9    D            `8  9              	  E           Degrees of the basic invariants `  x    F                         ;                                            9  `8  9  0  G  
         __sig__9   (  @  H            `8  9                I  
         BasicDegrees   T  J                 9                              K        8   The simple reflection matrices for a given Cartan matrix       L                                                                     89  `8  ,9  8!  M  
      	   __sig__10   0"  X"  N            `8  49              #  }  
      	   __sig__19       ~            `8  9                  
         LongestElement  	                   @:                                      G   The longest word in W as a reduced expression in the simple reflections d  |                             ;                                           `:  `8  T:      
      	   __sig__24     (              `8  \:              x    
         LongestWord   @                   X:                                      T   The set of indices of generators s such that the length of sw is less than that of w !  <!                               ;                                     x:  `8  l:  $    
      	   __sig__25   t%  %              `8  t:              &    
         LeftDescentSet  (                   p:                                      '   The unique long root of greatest height /  (/  P/                           ;                                u           :  `8  :  p2    
      	   __sig__26   3  3              `8  :              L5    
         HighestLongRoot 7    
      	   __sig__27   @9  9  O           SimpleReflections   %  %  P                 09                              Q        '   The root system for the Cartan matrix C +  +  +  R                                                          0       X9  P9  `8  D9   0  S  
      	   __sig__11   81  P1  T            `8  L9              2  U        '   The root system for the Coxeter group W 4  4  5  W  
      	   __sig__12   6  6  [  
      	   __sig__13    9  (9  i        @   Convert a permutation p representing an element of W to a matrix     P  j                             ;                                     9  `8  9  (  k  
      	   __sig__16   (  @  l            `8  9              `  m  
         PermToMatrix   h  n                 9                              o           The squares of the root lengths T  l    p                         ;                                           9  `8  9    q  
      	   __sig__17       r            `8  9                  
         CoxeterGroup                      9                                      1   The finite Coxeter group of a given Cartan matrix   
  
                                                            ;      :  :  `8  :  d    
      	   __sig__20   T  l              `8  :                        :   The finite Coxeter group of a given compound type and rank    x                                                            ;           :  `8  :  H    
      	   __sig__21                   `8  :                        S   The length of the permutation `w` as a reduced expression in the simple reflections #  #                               ;                                     0:  `8  $:  X&    
      	   __sig__22   @'  '              `8  ,:              )    
         CoxeterLength   $,                   (:                                      <   The longest element in W as a permutation of the root system 1  1                           ;                                           H:  `8  <:  5    
      	   __sig__23   6  6              `8  D:              9  s  
      	   RootNorms   !  <!  t                 9                              u        4   The maximum of the squared lengths of the roots of W %  %  v                         ;                                           9  `8  9  X)  w  
      	   __sig__18   +  +  x            `8  9              -  y  
         MaxRootLength   /  z                 9                              {        1   The finite Coxeter group of a given type and rank   3  <4  |                                                        ;      :  9  `8  9  8          ?   The reflection subgroup of W generated by the given reflections     P                               ;                          ;          ;  `8  :  (    
      	   __sig__31   (  @              `8  ;              `                               U                          UZ      B  |B  A  pB                A  xB              $          "   The Nagata automorphism of 3-space                               Q                                Z          B  A  B                A  B                           NagataAutomorphism  !  8!                   B                                      F   The projectivity of A determined by the matrix of base ring elements M  $&                           D    Q                          Z          B  A  B  *    
      	   __sig__13   8,  X,              A  B              .    
         Projectivity /  /                   B                                      3   /usr/local/magma-2.5/package/AlgGeom/map/aut_proj.m DhE        3   /usr/local/magma-2.5/package/AlgGeom/map/aut_proj.m DhE  
         __sig__0 9  9  9  O           Range nt l             HighestShortRoot   L  d                   :                                &      ~   The element in the coset H x which keeps all positive roots of H positive. This is the coset representative of shortest length                                 ;                                     :  `8  :      
      	   __sig__28     ,              `8  :              x    
      
   SpecialRep                        :                                      :   The ordered set of special coset representatives of H in W                               ;   ;                          0           :  `8  :  "    
      	   __sig__29   #  #              `8  :              %             SpecialTransversal  &  &                   :                                      C   The list of all reflections in W as permutations of the root system .   .                           ;                                           :  `8  :  2    
      	   __sig__30    3  83              `8  :              4    
         Reflections $6  l6                   :                                         Kform m ts                   :                                      (   The unique short root of greatest height                                     ;                                u           :  `8  :                  `8  :                    (         Returns a triple f, A, X where the map f : W -> A gives the action of W on its standard G-set X; (in version 0, f is not returned)  	  	    
      	   __sig__35     (              `8  d;              p  O                         Y   Y                                 LA  DA  @        Q            @  @A                R        X   True iff f and g are defined by the same functions and have the same domain and codomain   t    S                         0   0                                 P  TA  @  HA  x  T  
         __sig__7   p    U            @  PA              x!  V        .   /usr/local/magma-2.5/package/AlgGeom/map/aut.m hQW        .   /usr/local/magma-2.5/package/AlgGeom/map/aut.m hQX        ,   True iff the domain and range of f are equal (  t(  Y                         Y                                           lA  \A  `A  \-  Z  
         __sig__0 /  $/  L/  [            \A  hA              0  \  
         IsEndomorphism  2  ]                 dA                              ^        U   True iff f is an automorphism of its domain; if so, the inverse of f is also returned   $9  `  
         __sig__1 :  L:  d:             degree                ReflectionSubgroup  H  `                    ;                                      *   True is W is a crystallographic Weyl group  
  
                           ;                                            ;  `8  ;      
      	   __sig__32                   `8  ;                           IsCrystallographic                       ;                                      E   The degrees of the basic invariants for a crystallographic Weyl group                              ;                                           8;  `8  ,;       
      	   __sig__33    "  "              `8  4;              x#    
         CrystalDegrees  $                   0;                                      O   The orbit of the n-th simple root under the action of the first n-1 reflections +   ,   ,                                                          0            P;  `8  D;  l0    
      	   __sig__34   1  1              `8  L;              2    
         StandardRoots   h4                   H;                                                       ;                                  0           h;  `8  \;  :                           ;                                           ;  ;  ;      
         __sig__1 	  T	  l	              ;  ;              
    
         DualKillingForm                    ;                                      C    The value of the Killing form on the root elements e_alpha, e_beta                                        ;                               ;  ;  ;      
         __sig__2   l                ;  ;                                 ;                                
         __sig__4 ant               +   The structure constant for [e_alpha,e_beta] "  "                           u    u    ;                               ;  ;  ;  $&    
         __sig__3 &  &  '              ;  ;              T)             LieStructureConstant ,   ,                    ;                                &      ~   The standard graph automorphism of W as a permutation of the roots and a sequence of signs for the action on Lie root elements  3                           ;                                            <  ;  <  t8              ;  <              4:             GraphAutomorphism   <;  T;  l;  ;    
         StandardAction                      `;                                      .   The Coxeter group W as a real reflection group  
                           ;                                 j           ;  `8  t;  `    
      	   __sig__36   P  h              `8  |;                  
         ReflectionGroup (                   x;                                      A   The fundamental weights with respect to the basis of simple roots   \  |                           ;                                           ;  `8  ;  h     
      	   __sig__37   !  !              `8  ;              #             FundamentalWeights   $  X$                   ;                                      )   /usr/local/magma-2.5/package/GrpCox/Lie.m   _a     "   )   /usr/local/magma-2.5/package/GrpCox/Lie.m   `a        8   The Killing form of the Cartan algebra with Weyl group W 0  0  0                           ;                                           ;  ;  ;  3    
         __sig__0 4  4  5              ;  ;               7          D   The Killing form of the dual of the Cartan algebra with Weyl group W :  :  9        %   True iff f and g have the same domain     :                         0   0                                     @  @  @  <
  ;  
         __sig__1   L  d  <            @  @                =                         Y   Y                                 A  @  @      D  >  
         __sig__2       ?            @  @              X  @  
         SameCodomain   x  A                 @                              B        '   True iff f and g have the same codomain L  d  |  C                         0   0                                     A  @  A  !  D  
         __sig__3 "  #  #  E            @  A              \$  F                         Y   Y                                 0A   A  @      '  G  
         __sig__4 )  )  )  H            @  A              \,  I  
      	   SameRange   -  -  J                 A                              K        '   True iff f and g have the same codomain p2  2  2  L                         0   0                                     8A  @  ,A  l6  M  
         __sig__5 8  8  8  N            @  4A              h:  P  
         __sig__6 ;  @;  X;  U           Regular                     <                                *         The matrix of ad(e_alpha) acting on X (on the right), where X is an indexed set of positive roots or an indexed set of negative roots for W                              0    u    ;                               (<  ;  <    	  
         __sig__5       
            ;  $<              t    
         LieRootMatrix   t                    <                                &      }   List of triples giving the position and value of the non-zero entries of the matrix of ad(e_alpha) acting on X (on the right)   h                            0    u    ;                               @<  ;  4<  x#    
         __sig__6 $  $  $              ;  <<              T&    
      
   LieRootElt  <'  |'                   8<                                      B   The matrix for the adjoint action of e_alpha (acting on the right)  $/  L/                           u    ;                                     X<  ;  L<  l2    
         __sig__7 3  3  3              ;  T<              H5    
         AdjointAction    7                   P<                                
         __sig__8 :  ;  $;          \   The sequence of elliptic curves with label S (e.g. "101A") in the elliptic curve database D.                                  5                                 @>  8>  =  ,>                =  4>                   "      g   The sequence of elliptic curves of conductor N and label S (e.g. "A") in the elliptic curve database D.   (                                     5                               H>  =  <>  \    
         __sig__8     ,              =  D>                        Y   An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D.   !  !                               5                                 `>  X>  =  L>  $    
         __sig__9 %  %  $&              =  T>              |'           _   The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. \-  -  -                                       5                       h>  =  \>  1    
      	   __sig__10   2  2              =  d>              h4          >   The number of curves isogeny class defined by S (e.g. "101A").  t8                               5                                 >  x>  =  l>  ;    
      	   __sig__11   t<  <              =  t>              =  u  
         LiftIsogeny H  `  v                 =                              w        9   Lift the isomorphism m to be defined over the base ring K   H  `  x                                                                  =  =  =    y  
         __sig__3       z            =  =                {  
         LiftIsomorphism $  |                 =                              }        D   Returns the zeta function of E at the prime p in the indeterminate q     ~                                |                              >  =  =  8!    
         __sig__4 "  0"  X"              =  =              #          G   Return the order of E with the base (finite) field extended by degree d &  &  &                               |                                      >  =  >   ,    
         __sig__5 -  -  -              =  >              /          H   The sequence of elliptic curves corresponding to linear Hecke subspaces.     |                                                                        >    >  6             __sig__9             9             CremonaReference :  :  :                                                   
         __sig__7 =  \=  t=  X                 P=                              Y        %   Get the current object of the process 4    Z                                                                   p=  8=  d=    [  
         __sig__2 7       \            8=  l=              7^                 h=                              _        .   The Label of the current object of the process    `                                                                   =  8=  |=      a  
         __sig__3      +7b            8=  =                 c  
         CurrentLabel 7    d                 =                              e        )   /usr/local/magma-2.5/package/EC/dummy_c.m   {|i           __sig__0                    M        .   /usr/local/magma-2.5/package/Process/process.m N        .   /usr/local/magma-2.5/package/Process/process.m O        (   True if no objects remain in the process   |    P                                                                b  H=  8=  <=  4  S        )   Advance to the next object in the process       T                                                                 X=  8=  L=    U  
         __sig__1   p    V            8=  T=                f        )   /usr/local/magma-2.5/package/EC/dummy_c.m   `~g  &      z   Returns true iff seq defines a point on the elliptic curve E when the base ring is K. Also returns the point if it exists.  #  $  h                                |                      ~       =  =  =  =  '  j            =  =              )  k  
         IsRationalPoint $,  l                 =                              m  B         For E be an elliptic curve on the base ring R, returns true iff seq defines a point on the elliptic curve E on the base ring is K, where f : R -> K is used to coerce the elements of the sequence into K; also returns the point if it exists  8  n                                    |                ~           =  =  =  ;  o           __sig__1 <  <  <  <   =  :                 <                              ;         e   Returns four sequences of functions indexed by the simple roots: x_a(t), x_[-a](t), n_a(t) and h_a(t)   d  <                                                                      <  ;  <    =  
      	   __sig__14       >            ;  <                ?           ChevalleyFunctions  @  X  @                 <                              A         _   The order of the finite Chevalley group of given type and rank over the finite field of order q   4  l  B                                                                 =  ;  =  \"  C  
      	   __sig__15   d#  |#  D            ;  =              $          0   /usr/local/magma-2.5/package/EC/SEA/sea_header.m           .   /usr/local/magma-2.5/package/EC/SEA/sea_main.m         .   /usr/local/magma-2.5/package/EC/SEA/sea_main.m         >   The order of E using the methods of Schoof, Elkies, and Atkin.                             |                                            >  >  >  (                   >                                      0   /usr/local/magma-2.5/package/EC/SEA/brent-kung.m           0   /usr/local/magma-2.5/package/EC/SEA/brent-kung.m   @           Return f(g) mod h                                                                      >  >  >  >  #    
         __sig__0 $  $  $              >  >              &             ModularComposition  $(  t(                   >                                <         Return the r-th iterate of composition of f with itself modulo h, computed using the Brent-Kung machinery (assumes that f defines and endomorphism of the quotient by h, so that modular composition is well-defined)   h4                                                                   >  >  >  $9    
         __sig__1 :  L:  d:              >  >              ;          $   /usr/local/magma-2.5/package/HC/hc.m ʸE  
         ChevalleyOrder  &  F                 =                              Q  
         __sig__0 Order  +  G  "      h   The factored order of the finite Chevalley group of given type and rank over the finite field of order q 0  0  1  H                                                                 (=  ;  =  h4  I  
      	   __sig__16   `5  x5  J            ;  $=              t8  K           FactoredChevalleyOrder  4:  L                  =                              R            8=  D=              <                   8@                                      )   /usr/local/magma-2.5/package/FldRe/real.m   h     
   )   /usr/local/magma-2.5/package/FldRe/real.m   h        W   A value y and an error estimate dy, such that p(x) = y where p(xa[i]) = ya[i] for all i 0  P  h                           V   V   V                     V V           `@  P@  T@      
         __sig__0                   P@  \@                        \   Approximation to integral of real function f from a to b, using Romberg's method of order 2k   h                           V    V                        V           p@  P@  d@  X"    
         __sig__1 #  `#  x#              P@  l@              $             RombergQuadrature   l&  &                   h@                                       b   Approximation to integral of real function f from a to b using Simpson's rule with n sub-intervals  $/  L/                                V    V                  V           @  P@  |@  l2  !  
         __sig__2 3  3  3  "            P@  @              H5  #           SimpsonQuadrature   7  `7  $                 @                              -  
         __sig__4 ture   T;  %        V   Approximation to integral of f from a to b using trapezoidal rule with n sub-intervals  >                   ?                                      6   Returns false if shown to be ordinary, true otherwise.  	                           |                                            ?  d?  ?      
         __sig__2                   d?  ?                           IsProbablySupersingular                    ?                                      4   /usr/local/magma-2.5/package/EC/SEA/torsion_module.m X        1   /usr/local/magma-2.5/package/EC/SEA/trace_table.m .mxX        ,   /usr/local/magma-2.5/package/EC/SEA/shanks.m X             @  @              kage  
         BaerDerivation  ˸                 @                                      >   A translation plane from PG(2, q) by derivation w.r.t. an oval  (                                                                         (@   @  @  -  	  
         __sig__1 /  d/  |/  
             @  $@              1    
         OvalDerivation  <2                    @                                         A Baer subplane of PPl  5                                                                         @@   @  4@  :    
         __sig__2 ;  l;  ;               @  <@              <    
         BaerSubplane =  =             OptimalModularCompositionSetup                       ?                                $      o   Given setup information for a polynomial g and modulus h, set g_r to be the r-th self-composition of g modulo h  4                                                                       ?  >  ?  05    
         __sig__3                     >  ?                             OptimalModularCompositionApply                       ?                                      ,   /usr/local/magma-2.5/package/EC/SEA/schoof.m    7          ,   /usr/local/magma-2.5/package/EC/SEA/elkies.m   7        (   /usr/local/magma-2.5/package/HC/jac_hc.m  .m .m   
         __sig__0 age/EC/SEA/p            =  =                  q        5   Lift the isogeny m to be defined over the base ring K   RH3r                                                                  =  =  =     s  
         __sig__2   >5?3    t            =  =                        C   The number of curves of conductor N and isogeny class S (e.g. "A").                                         5                               >  =  |>  84  
      	   __sig__12      ,              =  >                          -   The trace of the Frobenius endomorphism of E.                               |                                            >  =  >  1    
      	   __sig__13                    =  >                             TraceOfFrobenius 7                        >                                          ?  ?                             __sig__1          L        (   /usr/local/magma-2.5/package/EC/SEA.spec    7                 /home/was/magma/spec RngLoc/            D?  P?              SEA/atkin.m         +   /usr/local/magma-2.5/package/EC/SEA/atkin.m ig m      
         __sig__0                    -   /usr/local/magma-2.5/package/EC/SEA/lercier.m             -   /usr/local/magma-2.5/package/EC/SEA/menezes.m   l	              Change pt1 to pt1 + pt2.  /shanks.m        7   /usr/local/magma-2.5/package/EC/SEA/modular_equations.m H        7   /usr/local/magma-2.5/package/EC/SEA/modular_equations.m H        5   Return the canonical modular equation for the prime l                                                                          T?  D?  H?                     L?                                      3   /usr/local/magma-2.5/package/EC/SEA/supersingular.m H        3   /usr/local/magma-2.5/package/EC/SEA/supersingular.m H        1   Returns true if ordinary, false if supersingular.   %  $&                           |                                            t?  d?  h?  *    
         __sig__0 ,  8,  X,              d?  p?              .    
      
   IsOrdinary  /  /                   l?                                      /   Returns true if supersingular, false otherwise. h4  4  4                           |                                            ?  d?  ?  9    
         __sig__1 :  |:  :              d?  ?              ;    
         IsSupersingular <    
         __sig__0 ngular =          F   Return setup information for optimal compositions of g with modulus h.                                                                       ?  >  >  `    
         __sig__2   X  p              >  ?                _                         Y                                 Y      LC  A  \A  xA    a            \A  A              	  b  
         IsAutomorphism  
  c                 |A                              d        2   /usr/local/magma-2.5/package/AlgGeom/map/aut_aff.m  he        2   /usr/local/magma-2.5/package/AlgGeom/map/aut_aff.m  n  
         __sig__1 ism     f           The identity automorphism on A  \  g                         P                                Y          A  A  A  H  h  
         __sig__0       i            A  A              8!  j           IdentityAutomorphism "  "  k                 A                              l        M   The linear automorphism of A determined by the matrix of base ring elements M   '  m                         D    Q                          Z      A  A  A  A  ,  o            A  A              L/  p        1   The automorphism which translates p to the origin   1  1  q                         T   Q                          Z      TB  A  A  A  5  r  
         __sig__2 6  6  6  s            A  A              9  t  
         Translation |:  :  u                 A                              v        :   The automorphism which exchanges the first two coordinates  ?  $?  x  
         __sig__3 @  @  @                               R                          \          C  B  C      
         __sig__5 	  X	  p	              B  C              
          B   The image of S under the translation of p to the point [0:...:0:1]  L  d                           T   V                          V\          ,C  B   C      
         __sig__6                   B  (C                  
         __sig__8 nity              a   Translate the point p to the point [0:1:0] and the tangent line to C at p to the line at infinity                                T   X                          X\          <C  B  0C  "    
         __sig__7 #  #  #              B  8C              L%             TranslationToInfinity   &                   4C                                      I   True iff f is a linear automorphism of some projective space over a field   .   .                           \                                           TC  B  HC  2              B  PC              l3          (   The matrix determining f if it is linear 5  5  5                           \                                D           dC  B  XC  :    
         __sig__9 ;  p;  ;              B  `C              <             The inverse of f =  (>  >                           \                                           tC  B  hC  B  w                         Q                                Z      dB  A  A  A      y            A  A                 z  
         FlipCoordinates    {                 A                              |        V   The automorphism (x,y,...) -> (x+p,y,...) where p is a polynomial on A not involving x  +7}                             Q                          Z      B  A  A  A     ~  
         __sig__4   +7                A  A                  
         __sig__6 rphism            B   The automorphism of A that permutes its coordinates according to g                                       Q                          Z          B  A   B  4?    
         __sig__5       >              A  B                             PermutationAutomorphism                     B                                      B   The automorphism of A that permutes its coordinates according to g                                                                        ?  ?  ?                Change pt1 to pt1 - pt2.                                                                      ?  ?  ?                  ?  ?                             Change pt to n*pt.    d5                                                               ?  ?  ?       
         __sig__2   7                ?  ?                        (   /usr/local/magma-2.5/package/HC/kum_hc.m    pp        )   /usr/local/magma-2.5/package/Plane/geom.m   p         )   /usr/local/magma-2.5/package/Plane/geom.m    p        Q   An affine plane constructed by the technique of derivation w.r.t. a Baer subplane   0?                                                                             @   @  @       
         __sig__0                                          Q                          Z      ,B  $B  A  B                A   B              	          :   The automorphism determined by the sequence F of functions  ,  D                               Q                          Z      tB  4B  A  (B      
         __sig__7                   A  0B                        :   A linear endomorphism l and a translation t with f = t o l  x                             Z                                ZZ      e  DB  A  8B  |    
         __sig__8   t                A  @B              |!             AffineDecomposition "  "                   <B                                      7   The image of S under the translation of p to the origin  '  @'  '                           T   U                          UZ      B  \B  A  PB  ,    
         __sig__9 -  .   .              A  XB              p0           d   The image of S under the automorphism which exchanges the first two coordinates of its ambient space 4  l4                           U                                UZ          lB  A  `B  (9    
      	   __sig__10   P:  h:              A  hB              ;          7   The image of S under the atomic automorphism given by p =  =  =    
      	   __sig__11   ?  ?    
      	   __sig__12   A  (A              E  LF                        :   The map of ambient spaces determined by the functions in F                                     R   Q                    [      V  `F  E  TF  l    
         __sig__2                    E  \F                                            Q                          QZ      tF  lF  E          
         __sig__3                    E  hF                        U   The base change of A to K induced by the automatic coercion of coefficients of A to K                                 R                          Q\      F  |F  E  pF  P    
         __sig__4      d              E  xF              `                               Q                          QZ      F  F  E      h    
         __sig__5      |              E  F              h*          @   The base extension of A determined by the map i of its base ring 1     d1                               R                          R\      I  F  E  F  8    
         __sig__6 8     ,8              E  F              D8                                Y                                     F  E      C    
         __sig__7 C     C              E  F              =z2           Print the map f                                  0                                          @D  C  4D  0    
         __sig__7                     C  <D                  6                 D                              8                         0                                Y          D  C  D  8
  :            C  D                <                 D                              =        0   The functions defining an ambient map covering f   (  @  ?  
      	   __sig__15                  HackobjCoerceAmbMap <  T                   F                                
      	   __sig__14 rtMap                                  Z                                     F  E          
         __sig__8                      E  F              X"             HackobjCoerceAmbAffMap  #                   F                                                            [                                     F  E      )    
         __sig__9 +   ,   ,              E  F              -             HackobjCoerceAmbChartMap /  40  l0                   F                                                            \                                     F  E      x5    
      	   __sig__10   7  `7              E  F              9             HackobjCoerceAmbProjMap $;                   F                                         Print f at level l  $>  >                              Z                                    F  E  F  B    
      	   __sig__11   D  D  ,                        3                                          D  C  D     /           SchChartMapPrint       7  0                 D                              1        H   True if and only if f is known to be the restriction of some ambient map       7  2                         0                                
           D  C  D      3  
      	   __sig__13   >      4            C  D                 A           AmbientDefiningFunctions 7       B                 D                              C           The domain of f a7       D                         0                                S       H  E  C  E  a7F            C  E                 G           The codomain of f      ?  H                         0                                S      0H  (E  C  E      I  
      	   __sig__17   A      J            C  $E                 K           The codomain of f                   F   The automorphism of P determined by the matrix of base ring elements M  <	                              R                          \      C  B  B  B  @              B  B              `    
         __sig__2 lex   h          N   The translation taking the standard simplex of P to the dim(P) + 2 points of S                            T   R                          \          B  B  B      
         __sig__1   \  |              B  B              x             TranslationOfSimplex                      B                                      N   A translation taking the points [0:..1:..0] of P to the dim(P) + 1 points of S  H%                          T   R                          \      B  B  B  B  $)              B  B              +          (   A linear automorphism of P taking p to q .  .  /                           T   T   R                    \      C  B  B  B  <2    
         __sig__3 3  P3  h3              B  B              5          <   A linear automorphism of P taking the point [0:...:0:1] to p 9  9                           T   R                          \      $C  C  B   C  ,<    
         __sig__4 <  =  ,=              B  C              $?          :   The automorphism determined by the sequence F of functions  HB  B    
         SchMapPrint                      8D                                         Print the map f l	  	  	                          0                                          XD  C  LD      
         __sig__8   x                C  TD                           SchMapPrintMaximal                       PD                                         Print the map f                               1                                          pD  C  dD      
         __sig__9                   C  lD                   
         SchAffMapPrint  "                   hD                              '  
      	   __sig__11 mal   H%             Print the map f &  &  &                           1                                          D  C  |D  +  !  
      	   __sig__10   -  \-  "            C  D              |/  #           SchAffMapPrintMaximal   1  $                 D                              %           Print the map f h4  4  4  &                        2                                          D  C  D  9  (            C  D              :  )  
         SchProjMapPrint ;  *                 D                              +           Print the map f $?  X?  x?  -  
      	   __sig__12   @  @  .            C  D              B  @C  xC    
      	   __sig__10                    B  pC              P             InverseAutomorphism T	  l	                   lC                                      2   /usr/local/magma-2.5/package/AlgGeom/map/sch_map.m       0   2   /usr/local/magma-2.5/package/AlgGeom/map/sch_map.m             is_from_ambient     (    
         ambient_map l                C  C                        P   The map S - -> T defined by the functions of F defined on the ambient space of S   0  H                               U   U                    1      <F   D  C  C  !    
         __sig__3 "  "  "               C  C              $          .   The map S - -> Codomain(f) as a map of schemes  &                           U   Z                          1      D  D  C  D  +    
         __sig__4 ,  ,  ,              C  D              L/          6   Return the map S - -> Codomain(f) as a map of schemes.  1                           U   [                          3      (D   D  C  D  5    
         __sig__5 6  6  6              C  D              9  	        6   Return the map S - -> Codomain(f) as a map of schemes.  ;  
                         V   \                          2          0D  C  $D  >    
         __sig__6 @  D@  t@              C  ,D              B  5  
         IsRestriction     7        O   A map of ambient spaces which covers f if f is known to have arisen in this way p	  	  	  9  
      	   __sig__14   
  
  ;  
      
   AmbientMap      E  
      	   __sig__16 ctions   >                         0                                            E  C  D    @            C  D              x  }         c   The base change of S by the map of its base ring i together with the induced map of ambient schemes d5    ~                             S                          SY      J   J  I  I      
         __sig__5 6                   I  I              d5        >   The base change of the schemes in the sequence F to the ring K 5                                                            Y      J  J  I  J      
         __sig__6 d5                   I  J              	d5        K   The base change of the schemes in the sequence F by the map i of base rings                                                                 Y         J  I  J  0    
         __sig__7                     I  J                    
         __sig__0 ierstrass 5                         W                                       <J  ,J  I           
         __sig__8   *t6                I  (J                  
         Preimage                        J                                                       T   [                          U      J  J  pJ      `    
         __sig__5   X  p              pJ  J                                         T   \                          V      J  J  pJ          
         __sig__6     $              pJ  J              t                           T   1                          U      J  J  pJ          
         __sig__7                   pJ  J              h              The preimage of p under f    "  "                           T   2                          V          J  pJ  J  H%    
         __sig__8 &  l&  &              pJ  J              t(                           Z                                U       K  J  pJ      \-    
         __sig__9 /  $/  L/              pJ  J              0                           [                                V      K  K  pJ      84    
      	   __sig__10   (5  H5              pJ  K              `7              The Zariski closure of f(dom(f)) :  L:  d:                           \                                V      0K  K  pJ  K  <    
      	   __sig__11   $>  >              pJ  K              t@             The pullback f^*(S) A  B                           S   Y                          U      4N  (K  pJ  K  ,G    
      	   __sig__12   lH  H                          T   \                                 J  J  pJ  J       
         __sig__3 ,                     pJ  J              4-                           T   Z                          U      J  J  pJ            
         __sig__4    2                  pJ  J                             pJ  $K              7        &   The image f(S) under the isomorphism f                              S   Y                          S      V  8K  pJ  ,K  +7  
      	   __sig__13      7              pJ  4K                          5   /usr/local/magma-2.5/package/AlgGeom/map/projection.m         5   /usr/local/magma-2.5/package/AlgGeom/map/projection.m   $      q   The affine scheme obtained by eliminating the ambient variables whose indices appear in V from the equations of S   >  a7                            U                          U          PK  @K  DK       
         __sig__0 >  a7                @K  LK              >    
         Elimination                         HK                                      W   The linear projection P - -> Q which forgets the first dim(P) - dim(Q) coordinates of P                                   R   R                          \      pK  hK  @K  \K        
         __sig__1    @  7            @K  dK                   
         __sig__2 @  7                @K  tK                    
      	   functions 7         
         base_map 5           
         __sig__0          1           IsFace  x              standard_chart_map  @  
         linear_part                  translation_part            
         inverse p                                                              
      	   is_linear p    =    
         linear_matrix   >    
      	   is_affine 7                                                                                             function_degree <?  0P                                                                                                                                                    Q   Q                    Z      HF  DF  E      L@              E  @F                                               R   R                    \      XF  PF  E      @    
         __sig__1 7                  Minors tch  V                 HE                              W        ,   Declare f to be finite or not according to b 	  <	  X                            0                                0I  hE  C  \E  @  Y  
      	   __sig__20     0  Z            C  dE              h  \                 `E                              ]        8   Declare f to be generically finite or not according to b       ^                            0                                @I  E  C  tE    _  
      	   __sig__21   `  x  `            C  |E                a           GenericallyFinite   !  !  b                 xE                              c        $   Declare f to have (generic) degree d %  %  d                            0                                H  E  C  E  T)  e  
      	   __sig__22   +  +  f            C  E              -  g        4   Declare f to be an isomorphism or not according to b 0  0  h                            0                                `I  E  C  E  84  i  
      	   __sig__23   (5  H5  j            C  E              `7               L  ,L              Geomk        6   /usr/local/magma-2.5/package/AlgGeom/map/composition.m l     
   6   /usr/local/magma-2.5/package/AlgGeom/map/composition.m m        0   The composition (f o g): Domain(g) - -> Range(f) B  HB  B  o  
         __sig__0 D  D  D  L                         0                                S      @H  8E  C  ,E    M  
      	   __sig__18   	  	  N            C  4E              (  P                 0E                              Q        -   Declare f to be regular or not according to b     R                            0                                 I  PE  C  DE  $  S  
      	   __sig__19       T            C  LE              <              E  F              $             HackobjPrintAmbAffMap   T                   F                                         Print f at level l  L  d                              \                                    G  E  G      
      	   __sig__12                   E  G                           HackobjPrintAmbProjMap  X                   G                                         Print f at level l  x                                [                                    (G  E  G      
      	   __sig__13   !  <!              E  $G              "             HackobjPrintAmbChartMap #                    G                                ,         True iff f is one of the standard chart maps of its codomain; in this case the index of that map in the sequence of patch maps is also returned `-  -  -                           [                                            @G  E  4G  1              E  <G              2    
         IsStandardChart l4                   8G                                $      s   True iff f is defined by the same functions as a standard chart map; in this case also return the index of that map ;   <                           [                                            XG  E  LG  |?    
      	   __sig__15   @  @              E  TG              B             IsLikeStandardChart E  @E  n                         Y   Y                          Y      n  E  E  E    q                         \   \                          \      E  E  E      "  r  
         __sig__1 #  #  #  s            E  E              %  t                         Z   Z                          Z      E  E  E      X)  u  
         __sig__2 +  +  +  v            E  E              -  w                         [   \                          [      E  E  E      1  x  
         __sig__3 2  2  2  y            E  E              l4  z        .   The composition (f o g): Domain(g) -> Range(f)  7  {                         Z   [                          [          E  E  E  (;  |  
         __sig__4 <  <  0<  }            E  E              x=  ~        2   /usr/local/magma-2.5/package/AlgGeom/map/amb_map.m  8     \   2   /usr/local/magma-2.5/package/AlgGeom/map/amb_map.m              E  G                           Faces                  E  G              h     
      
   AlgebraMap                       hG                              B                .   The natural underlying map of polynomial rings  
                           \                                           G  E  |G  0    
      	   __sig__17     0          ]   The common degree of the defining functions of f in their normalised, coprime polynomial form   t                           \                                           G  E  G      
      	   __sig__18         
         FunctionDegree  !                   G                                                       Z                                U      G  G  E      &    
      	   __sig__19   $(  t(              E  G              *    
      
   BaseScheme  x,  ,                   G                                                       [                                V      G  G  E      2    
      	   __sig__20   3  84              E  G              x5          8   The subscheme of the domain of f where it is not defined 9  9  9                           \                                V      U  G  E  G  <    
      	   __sig__21   =  =              E  G              ?          8   The subscheme of the domain of f where it is not defined B  @C  xC    
      	   __sig__22   E  <E              E  G              \G    
         inner_vertices       
         vertices          
         all_vertices                 lower_vertices             
         outer_vertices  D    
         outer_faces         
      	   all_faces          
         inner_faces        
         islinear            
         lower_faces      Q        ,   True iff p = <a,b> lies on the boundary of N      R                             b                                     PQ  P  DQ     T            P  LQ              8  U  
      
   IsBoundary     L  V                 HQ                              W        "   True iff p = <a,b> is a point of N        X                             b                                 (]  hQ  P  \Q  x  Y  
         __sig__6 *     `*  Z            P  dQ              x*  [        :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/npoly.m  !\        :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/npoly.m   !]        )   True iff N was defined using a polynomial      @8  ^                         b                                           Q  pQ  tQ  C  _  
         __sig__0 C     C  `            pQ  |Q              F  a  
         HasPolynomial   0F  e           __sig__1 N     N         /        :   True iff f is defined by polynomials of degree at most one      0                         Z                                           H  E  H  
  2            E  H              D  h                         R                                \      I  I  I  I    j            I  I                k           QuadraticTransformation (  l                 I                              m        I   The quadratic transformation of P in the linearly independent points of S       n                        T   R                          \      I  I  I  I  |!  o  
         __sig__1 "  "  "  p            I  I              #  q        H   The birational pullback of X under the standard quadratic transformation &   '   '  r                         V                                V      I  I  I  I  \,  s  
         __sig__2 -  -  -  t            I  I               0  u         b   The birational pullback of X quadratic transformation of P in the linearly independent points of S  3  <4  v                        T   V                          V          I  I  I  8  w  
         __sig__3 9   :  8:  x            I  I              X;  y         `   The base change of S to K by automatic coercion together with the induced map of ambient schemes ?  \?  |?  z                            S                          SY      I  I  I  I  `D  |            I  I              F             Closure `G                   PG                                      6   The underlying map of polynomial rings if f is regular                               Z                                       G  pG  E  dG        
      	   __sig__16                       E  lG                    
      
   BasePoints                        G                                         The functions used to define f  	                           Y                                           H  E  H      
      	   __sig__24                   E  H                           DefiningFunctions                        H                                         The domain of f   <  \                           Y                                P        (H  E  H  H  	  
      	   __sig__25       
            E  $H              8!             The codomain of f   "  "                           Y                                P        8H  E  ,H  %    
      	   __sig__26   &  &              E  4H              $)             The codomain of f   +  +                           Y                                P          HH  E  <H  /    
      	   __sig__27   41  L1              E  DH              2             True iff f is regular   h4                           Y                                           XH  E  LH  $9    
      	   __sig__28   L:  d:              E  TH              ;             True iff f is regular   <                           \                                           hH  E  \H  @    
      	   __sig__29   A  B              E  dH              D    
      
   IsMorphism  F  F    
      	   __sig__30   G  G                           Y                                S      U  G  E  G      
      	   BaseLocus   	  	                   G                                      Q   The sequence of base points of f if finite which are defined over the base field.   P  h                           Y                                       U  G  E  G      
      	   __sig__23                   E  G                O        8   Declare f to be generically finite or not according to b       P                            Y                                    HI  E  <I  
  Q  
      	   __sig__41       R            E  DI              4  S        $   Declare f to have (generic) degree d     T                            Y                                U  XI  E  LI  X  U  
      	   __sig__42   0  x  V            E  TI                W        4   Declare f to be an isomorphism or not according to b   L  X                            Y                                    hI  E  \I  !  Y  
      	   __sig__43   "  "  Z            E  dI              $  [           The identity map A -> A %  %  (&  \                         P                                Y          xI  E  lI  *  ]  
      	   __sig__44   <,  \,  ^            E  tI               .  _        $   The constant map A -> B with image p 0  0  `                         T   P   P                    Y          I  E  |I  <4  a  
      	   __sig__45   ,5  L5  b            E  I              d7  c  
         ConstantMap 9  9  d                 I                              e        2   /usr/local/magma-2.5/package/AlgGeom/map/special.m  (89f        2   /usr/local/magma-2.5/package/AlgGeom/map/special.m  x89{  
         __sig__4 mation B  g        :   The quadratic automorphism [x,y,...] -> [1/x,1/y,...] of P  F  F  i  
         __sig__0 G  G  G                   `H                                         True if f is known to be finite                                Y                                           H  E  tH  L#               E  |H              $  !            True iff f is generically finite &  &  &  "                         Y                                           H  E  H  +  #  
      	   __sig__31   -  `-  $            E  H              /  %           IsGenericallyFinite 0  1  &                 H                              '           The degree of f l4  4  4  (                         Y                                       PI  H  E  H  9  )  
      	   __sig__32   :  :  *            E  H              ;  +        6   True iff f is a morphism defined by linear polynomials  =  ,                         Y                                           H  E  H  B  -  
      	   __sig__33   xD  D  .            E  H              F  1        	   __sig__34   G  G   H  H  3  
         IsAffineLinear    4                 H                              5           True iff f is an isomorphism 	  	  6                         Y                                 Y          H  E  H    7  
      	   __sig__35       8            E  H                9        (   The inverse of f iff f is an isomorphism   H  t  :                         Y                                Y          H  E  H  <  ;  
      	   __sig__36   ,  D  <            E  H              H  =           True iff f is surjective       >                         Y                                            I  E  H  H#  ?  
      	   __sig__37    $  X$  @            E  H              $&  A           True iff f is dominant  |'  B                         Y                                           I  E  I  ,  C  
      	   __sig__38   .  .  D            E  I              l0  E  
      
   IsDominant  1  1  F                 I                              G        -   Declare f to be regular or not according to b   5  H                            Y                                    (I  E  I  :  I  
      	   __sig__39   l;  ;  J            E  $I              <  K        ,   Declare f to be finite or not according to b ?  x?  L                            Y                                    8I  E  ,I  \D  M  
      	   __sig__40   TE  lE  N            E  4I              G                              L                          L      R  R  0R  tR      
         __sig__4 	  X	  p	              0R  |R              
    (         The pullback of L by f; the second return value is a comparison map from the coefficient space of L to that of the pullback system                               L   \                          L           R  0R  R      
         __sig__5                   0R  R                  "      h   The subsystem of L for which the pullback by f contains the i-th coordinate hyperplane to multiplicity m   $   l                                    \   L              L          R  0R  R  |#    
         __sig__6 $  $  $              0R  R              X&             RestrictedSystem '  '  '                   R                                      ?   The subsystem of L of projective plane curves tangent to C at p P/  h/  /                           X   T   L                    L      V  R  0R  R  2    
         __sig__7 3  3  <4              0R  R              |5          >   /usr/local/magma-2.5/package/AlgGeom/linearsystem/elt_linsys.m  L        >   /usr/local/magma-2.5/package/AlgGeom/linearsystem/elt_linsys.m  L        '   True if and only if p is a section of L =  (>  >                               L                                     R  R  R  B    
         __sig__0 D  D  D              R  R               G    
      	   IsSection    H  H    
         __sig__1 J  J  XK             IsEllipticWeierstrass                       $J                                      3   True iff C is an elliptic curve in Weierstrass form 
  
                           X                                           DJ  I  8J      
         __sig__9                   I  @J                                         W                                       `J  PJ  I      t    
      	   __sig__10     <              I  LJ              |             IsHyperellipticWeierstrass                       HJ                                      7   True iff C is a hyperelliptic curve in Weierstrass form H#  `#  x#                           X                                           hJ  I  \J  &    
      	   __sig__11   $(  t(              I  dJ              *          0   /usr/local/magma-2.5/package/AlgGeom/map/image.m -  OR        0   /usr/local/magma-2.5/package/AlgGeom/map/image.m 1   PR           The image point f(p) 2  2                           T   Y                          T      J  J  pJ  tJ  h6              pJ  |J              $9                          T   Z                                 J  J  pJ      ;    
         __sig__1 <  <  <              pJ  J              >                          T   [                                 J  J  pJ      B    
         __sig__2 D  D  D              pJ  J              ,G             The sequence f(Z)   H  I  I  I           c   The image of the projection of S away from (1:0:...:0); the ambient projection map is also returned d5                             V                                V\      K  xK  @K  lK            Y   The image of the projection of S away from p; the ambient projection map is also returned   d5                             T   V                          V\          K  @K  |K      
         __sig__3 d5                   @K  K              d5        6   /usr/local/magma-2.5/package/AlgGeom/map/map_closure.m e        6   /usr/local/magma-2.5/package/AlgGeom/map/map_closure.m e        R   The natural map PA - -> P where f : A - -> P and PA is the projective closure of A                                  [                                \      K  K  K  K      
         __sig__0                     K  K                          9   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/ndef.m   V]        9   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/ndef.m   8W]  
         polynomial2 x      
         parent_ring                defining_points       b                 xQ                              c        D   The polynomial used to create N; an error if no polynomial was used.   t  d                         b                                      D^  Q  pQ  Q  D  f            pQ  Q              H  g  
      
   Polynomial      h                 Q                              i        Y   The parent ring of the polynomial used to define N; an error if a polynomial was not used    %  H%  j                         b                                           Q  pQ  Q  $)  k  
         __sig__2 *  @+  +  l            pQ  Q              \-  m  
      
   ParentRing  $/  L/  n                 Q                              o  &      }   The polynomial comprising those monomials of the defining polynomial of N that lie on face F; an error if N has no polynomial   h6  p                             b                                     Q  pQ  Q  :  q  
         __sig__3 ;  ;  ;  r            pQ  Q              <  s  
         FaceFunction >  >  t                 Q                              u        K   The maximum length of the x-projection of a face of the Newton Polygon of f TE  lE  v                                                                     Q  pQ  Q  TK                                                                   L  K  L               IsCoercibleMatrix   	  	                   L                              ]                 dq                                      $   A complement in L to the subsystem K stem/vs        >   /usr/local/magma-2.5/package/AlgGeom/miscellaneous/polyrings.m d     (   >   /usr/local/magma-2.5/package/AlgGeom/miscellaneous/polyrings.m d	        D   The polynomial comprising terms of f whose total degree is that of f     
                                                                     0L   L  $L  "    
      
   DegreeForm  #  #                   (L                                         The constant term of f  |'                                                                       HL   L  <L  ,    
         __sig__1 -  .  .               L  DL              l0    
         ConstantTerm 1  1                   @L                                      C   The linear term of f with respect to the grading on its parent ring 6   7                                                                       `L   L  TL  $;    
         __sig__2 ;  <  ,<               L  \L              t=    
      
   LinearTerm  ?  $?                   XL                                      J   The affine linear term of f with respect to the grading on its parent ring  F  F    
         __sig__3 G  G  G               L  tL              TK  K  K                   K                                       _   The natural map PA - -> PB where f : A - -> B and PA, PB are the respective projective closures 	  	  	                           Z                                \          K  K  K      
         __sig__1                   K  K                        <   The restriction of f to the jth affine patch of its codomain   $                               [                          Z      K  K  K  K      
         __sig__2                   K  K                           RestrictionToPatch      h                    K                                       d   The restriction of f from the ith affine patch of its domain to the jth affine patch of its codomain &  T&                                   \                    Z          K  K  K  *    
         __sig__3 ,  x,  ,              K  K              /          ;   /usr/local/magma-2.5/package/AlgGeom/miscellaneous/matrix.m 8il        ;   /usr/local/magma-2.5/package/AlgGeom/miscellaneous/matrix.m il        0   A sequence containing all the r by r minors of M 7  7  t8                               D                                      K  K  K  ;    
         __sig__0 <  t<  <              K  K              =                    K                                      Z   True if and only if all entries of M are coercible into S; in that case, also return 'S!M'  E  F    
         __sig__1 G  tG  G              K  L              TJ  J  TK  9  ,         True iff the compact convex hulls of the defining points of N and M have the same vertices and were defined in a similar way (see manual for details)   
  :                         b   b                                      P  P  P  4  ;  
         __sig__1     4  <            P  P                =  
         CompactlyEqual    >                 P                              ?  2         True iff the lower vertices of the compact convex hulls of the defining points of N and M have the same vertices and were defined in a similar way (see manual for details)     @                         b   b                                      Q  P  P  L#  A  
         __sig__2 $  $$  \$  B            P  Q              (&  C  
      
   LowerEqual   '   '  D                  Q                              E  2         True iff the outer vertices of the compact convex hulls of the defining points of N and M have the same vertices and were defined in a similar way (see manual for details) (2  @2  F                         b   b                                       Q  P  Q  |5  G  
         __sig__3 7  7  d7  H            P  Q              9  I  
      
   OuterEqual  :  :  J                 Q                              K        ,   True iff p = <a,b> lies in the interior of N ?  (?  L                             b                                     8Q  P  ,Q  |C  M  
         __sig__4 D  E  @E  N            P  4Q              `G  O  
      
   IsInterior  H  I  P                 0Q                              S           __sig__5 M  M  M   N  N  C                 T                              D        0   The degree of the polynomials used to generate L      $  E                         L                                       h^  U  ,T  U  p  G            ,T  U                H        3   A sequence of basepoints that were used to define L      I                         L                                           ,U  ,T   U    J  
         __sig__9        K            ,T  (U                L           DefiningBasePoints       M                 $U                              N        &   True iff L is a complete linear system  T  O                         L                                           DU  ,T  8U    P  
      	   __sig__10        Q            ,T  @U              l  Z  
      	   __sig__12 em    4(  R        '   The complete linear system containing L t*     x*  S                         L                                L          TU  ,T  HU  7  T  
      	   __sig__11      8  U            ,T  PU              $8  V           CompleteLinearSystem    <8  W                 LU                              X           The dimension of L     C  Y                         L                                       \  lU  ,T  `U  $F  [            ,T  hU              N  \           The space of coefficients of L  N  ^  
      	   __sig__13      N  _            ,T  xU                                                                           
         __sig__2 gon                                      b                                     N  N           
         __sig__0 =                     N  N              >             HackobjCoerceNwtnPgon 7                     N                                         Print polygon N at level l     <?                              b                                    N  N  N        
         __sig__1    ?                  N  N                            HackobjPrintNwtnPgon   a(5                 N                                      3   The Newton Polygon of a polynomial in two variables 7                                                              b      0O  O  N  N  @              N  O                    
         NewtonPolygon   7                  O                                
         __sig__3            %  
         GradedSubTerm     &                 L                              '        I   The terms of f of weight n with respect to the grading on its parent ring   H  `  (                                                                   L   L  L    )  
         __sig__5       *             L  L                +  
      
   GradedTerm    $  ,                 L                              -        P   A sequence containing all the derivatives of order m of all the polynomials in f   0  H  .                                                               L  L   L  L  !  /  
         __sig__6 "  "  "  0             L  L              $  1  
         AllDerivatives  %  2                 L                              3        9   A sequence containing all the derivatives of order m of f    ,   ,  4                                                                   L   L  L  l0  5  
         __sig__7 1  1  1  6             L  L              2  7        ]   The #I-th derivative obtained by differentiating with respect to the I[i]-th variable in turn   `7  8                                                                L   L  L  T;  9  
         __sig__8 <  D<  \<  :             L  L              =  ;         c   The polynomial f with all i-th variable factors removed; also returns the number of factors removed B  B  <                                                                    L   L  L  G  =  
         __sig__9 I  I  I  >             L  L              |L                                                                       xL   L  lL               AffineLinearTerm 	  	  	                    pL                              !        Q   The terms of f of weight at most n with respect to the grading on its parent ring       "                                                                   L   L  L  $  #  
         __sig__4       $             L  L              <  P             L  <M              $  Q        *   The lowest degree among the monomials of f      R                                                                     PM   L  DM    S  
      	   __sig__13       T             L  LM                U  $      t   The sequence of least degrees of f with respect to each different weighting given by the columns of the 2x2 matrix M     V                         D                                           `M   L  TM    W  
      	   __sig__14       X             L  \M                t                                                                     M   L  M  "  v             L  M              #  w           IsHomogeneouslyGenerated %  %  %  x                 M                              y        ;   /usr/local/magma-2.5/package/AlgGeom/miscellaneous/scheme.m h z        ;   /usr/local/magma-2.5/package/AlgGeom/miscellaneous/scheme.m  {        I   The subscheme of S of points at which the jacobian matrix of S drops rank    3  83  |                         S                                S          M  M  M  7  ~            M  M              9             JacobianSubrankScheme   :                   M                                      4   Compute a Groebner basis for the defining ideal of S ?  |?                          S                                          N  M  N  `D              M  N              F          \   Set the defining equations of S to be a Groebner basis of its defining ideal and return them L  PL  ?  
         RemoveFactor      @                 L                              A         c   The common denominator of the rational functions in F and the normalised sequence after its removal d#  |#  B                                                                    M   L  M  &  C  
      	   __sig__10   ((  x(  D             L  M              *  Y  
         MinimumDegrees    Z                 XM                              [        (   The polynomial term of least degree of f 
  `
  
  \                                                                     xM   L  lM  0  ]  
      	   __sig__15     0  ^             L  tM                _           MinimumDegreeTerm     (  `                 pM                              a        $   The polynomial term of degree d in f     b                                                                   M   L  M    c  
      	   __sig__16         d             L  M              "  e  
         HomogeneousTerm H#  f                 M                              o  
      	   __sig__18 ee &  &  g        :   The sequence of coefficients of monomials in f of degree d  )  *  h                                                                   M   L  M  L/  i  
      	   __sig__17   0  0  j             L  M              2  k           CoefficientsOfDegree 3  h3  l                 M                              m        8   The polynomial of R of degree d with coefficients from c 9  9  9  n                                                               M   L  M  <  p             L  M              =  q           PolynomialOfDegree  @  ,@  r                 M                                
         __sig__1 heme ed D  s        H   True iff the current set of generators of I are individually homogeneous H  H  I  u  
      	   __sig__19   K  L  }  
         __sig__0 L  M  ,M  E           CommonDenominator   -  -  F                 M                              G  $      v   The homogenisation of f in degree d with respect to z if this is possible with the grading on their common parent ring  4  H                                                             8M  (M   L  M  9  I  
      	   __sig__11   :  :  J             L  $M              ;  K  
         Homogenisation  <  L                  M                              M  "      j   The homogenisation of f with respect to z if this is possible with the grading on their common parent ring  E  <E  N                                                                   @M   L  4M  TJ  O  
      	   __sig__12   dL  |L          O   The Newton Polygon of a polynomial in one variable defined over a Puiseux Field                                                                 b           O  N  O                N  O                !        !   The Newton gradient of the face F   P  h  "                             b                                     P  P  P    $            P  P                %  
         Gradient   t    &                 P                              '        1   The set of faces that contain the point p = <a,b>   p    (                             b                                     P  P  P  #  )  
         __sig__6 #  #  $  *            P  P              %  +  
         FacesContaining &  ,                 P                              -  &      y   True iff F = <a,b,c> is a face of N (see handbook for details) in which case the normalised tuple of the face is returned   0  0  .                             b                                      P  P  P  3  /  
         __sig__7 4  4  5  0            P  P               7  2                 P                              3        :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/nbool.m  xx4        :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/nbool.m  Рx5         b   True iff N and M have the same vertices and were defined in a similar way (see manual for details)  D  D  6                         b   b                                  S  P  P  P  I  7  
         __sig__0 L  4L  LL  8            P  P              M                           S                                            N  M  N      
         __sig__2 	  	  	              M  N              (           f   Set and return the defining equations of S to be a minimal basis of its defining ideal and return them  h                           S                                           0N  M  $N      
         __sig__3                   M  ,N                                             Z                                 @N  <N  M      x    
         __sig__4   p                M  8N              x!                               [                                 PN  HN  M      X$    
         __sig__5 %  %  %              M  DN              '             The pullback f^*(p) <)  T)                               \                                 `N  XN  M  LN  .    
         __sig__6 /  /  /              M  TN              1             The pullback f^*(I) 2  2                               Y                                 R  hN  M  \N  6    
         __sig__7 8  8  $9              M  dN              :                           T                                    |N  tN  M      ,=    
         __sig__8 >  >  >              M  pN              @             Evaluate f at the point p   B  B                           T                                      N  M  xN  G    
         __sig__9 I  I  I              M  N              |L             polynomial1 M  M  M  M          =   /usr/local/magma-2.5/package/AlgGeom/linearsystem/vs_linsys.m       
         is_elliptic                 divisor_group                       is_hyperelliptic                    The affine plane curve f = 0                  divisor_class_group    l    
                                                      Q                          W      W  DW  W  8W      
         __sig__0                    W  @W                        2   The union of C and D in their common ambient space                                 W   W                          W      W  TW  W  HW  4    
         __sig__1      H              W  PW              `    
         __sig__3 ffPl   t          &   Create the place at the simple point x                                  W                           _          dW  W  XW  4(    
         __sig__2 *     h*              W  `W              *             HackobjCoerceCrvAffPl   d1                   \W                                      I   True iff the point x lies on S or the sequence of coordinates x lies in S      88                           W                                          |W  W  pW  C              W  xW              C             HackobjInCrvAffPl      F                   tW                                
         __sig__5 fPl    N             Print the curve C at level l    N                              W                                    W  W  W  `T  N                  M             Print L at level l  O  O    
         __sig__0 P  P  P              ,T  lT              @R  R  R                   R                                      7   True if and only if S is a hypersurface in the system L 	  	  8
                           S   L                                     R  R  R                 R  R              0    
      	   IsElement   (  @                   R                                      N   The unique line in the projective plane P through the points of S if it exists  <                          T   R                          X      ,S   S  R  R      
         __sig__2                   R  R              !          O   The unique conic in the projective plane P through the points of S if it exists $  $  $                          T   R                          X          S  R  S  (    
         __sig__3 *  *  *              R  S              ,          C   The unique hypersurface of degree d passing through the points of S 0  0                          T       R                                S  R  S  84    
         __sig__4 5  (5  H5              R  S              `7    
         SchemeThrough   9                   S                                                       T   T   X                    X      <S  4S  R      >    
         __sig__5 ?  @  ,@              R  0S              A          '   The line through p and q as points of C D  E  <E                           T   T   W                    W      [  DS  R  8S  TJ    
         __sig__6 L  dL  |L              R  @S              M  \           UniformizingElement /AlgGeom           sign ʸ  
         __sig__0 Q  Q  Q  y  
         MaxFaceLength      z                 Q                              {        H   True iff N is the Newton Polygon of f (see handbook for precise meaning) 7       |                            b                                      Q  pQ  Q  a(5}  
         __sig__5       L@  ~            pQ  Q                             IsNewtonPolygonOf      @                   Q                                      4   True iff the face function along F is not squarefree @  7                             b                                  R  R  pQ  R       
         __sig__6 @  7                pQ  R              @    
         IsDegenerate       ~           IsFree   s                           b                                           O  PO  O      
         __sig__3 	  T	  l	              PO  O              
    
         LowerVertices                      O                                      <   All vertices of the compact hull of the defining points of N                              b                                           O  PO  O  t    
         __sig__4     <              PO  O              |              P  ,P              x    
      
   InnerFaces  p                     (P                                      4   Those faces of N of points with minimal y coordinate #  $                           b                                           HP  P  <P  |'    
         __sig__2 )  <)  T)              P  DP               ,    
      
   LowerFaces  -  -                   @P                                      9   All faces of the compact hull of the defining points of N   2  2                           b                                           `P  P  TP  6    
         __sig__3 8  8  $9              P  \P              :    
         AllFaces ;  l;  ;                   XP                                      &   The Newton gradients of the faces of N  ?                           b                                           xP  P  lP  D    
         __sig__4 E  E  F              P  tP              G    
      	   Gradients   0J  TJ                    pP                              #           __sig__5 N  N  O  $O  dO    
         GBNewtonPolygon                     O                                      !   The Newton Polygon of the curve C   `
  
                           W                                b      @O  8O  N  ,O  0    
         __sig__4     0              N  4O                        7   The polygon which is the convex hull of the points of V T  l                                                              b          HO  N  <O      
         __sig__5                   N  DO                        :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/nvert.m  h        :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/nvert.m  h        -   The set of points used in the definition of N   &                           b                                           `O  PO  TO   ,    
         __sig__0 -  -  -              PO  \O              /    
         DefiningPoints  1                   XO                                         The vertices of N   4  4                           b                                           xO  PO  lO  9    
         __sig__1 :  |:  :              PO  tO              ;          /   Those vertices of N that lie nearest the origin =  =  =                           b                                           O  PO  |O  B    
         __sig__2 D  tD  D              PO  O              F    
         InnerVertices   G                   O                                      /   Those vertices of N having minimal y coordinate N  N  O                   z                                       d   Returns an expression in terms of Manin symbols for the element v in the space M of modular symbols. 
  
                           u    t                                      z  8s  z      
      	   __sig__84                   8s  z                  :         Returns an expression in terms of modular symbols of the element v in the space M of modular symbols. We represent a point in P^1(Q) by a pair [a,b]. Such a pair corresponds to the point a/b in P^1(Q).   0  H                           u    t                                      z  8s  z  !    
      	   __sig__85   "  "          4 8s  z  X   d         $             ConvToModularSymbol %  %                   z                                      2   Return the basis of M in terms of modular symbols.   ,   ,                           t                                            {  8s   {  l0    
      	   __sig__86   1  1          4 8s  {  X   l         2             ModularSymbolsBasis 4  4                   {                                                           t                           u       ,{   {  8s      $;    
      	   __sig__87   <  ,<              8s  {              t=             ConvFromManinSymbol X?  x?                   {                                                           t                           u       <{  4{  8s      F    
      	   __sig__88   G  H              8s  0{              K                                   t                     u           D{  8s  8{  O  O  O    
         AllVertices                       O                                       b   All vertices of the compact hull of the defining points of N together with the origin of the plane  (  @                           b                                           O  PO  O      
         __sig__5                   PO  O                  
         OuterVertices                      O                                      C   The two end vertices of the face F = <a,b,c> in anticlockwise order                                  b                                      O  PO  O  "    
         __sig__6 #  0#  H#              PO  O              $          #   True iff p = <a,b> is a vertex of N &  &                               b                          
           O  PO  O  +    
         __sig__7 ,  -  \-              PO  O              |/    
         IsVertex 0  0  0                    O                                      :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/nface.m  xH        :   /usr/local/magma-2.5/package/AlgGeom/newtonpolygon/nface.m  H  
         The faces of N  :                           b                                           P  P  P  =    
         __sig__0 ?  X?  x?              P  P              $A                   P                              	        &   Those faces of N which face the origin  ,G  
                         b                                           0P  P  $P  |L    
         __sig__1 M  M  M  3        =   /usr/local/magma-2.5/package/AlgGeom/curve/intersection_crv.m     4           True iff p lies on both C and D l	  	  	  5                         T   S   S                               X  X  X    6  
         __sig__0   x    7            X  X                8  
         IsIntersection    9                 X                              :                         T   W   W                            Y  X  X      ,  ;  
         __sig__1       <            X  X              h  =  
         IsTransverse    h   >                 X                              ?        ,   True iff C and D intersect transversely at p $  X$  @                         T   X   X                               Y  X  X  '  A  
         __sig__2 )  )  )  B            X  Y              X,  C                         T   X   X                           Y  Y  X      0  D  
         __sig__3 1  1  1  E            X  Y              43  F        8   The local intersection number of the curves C and D at p 5   6  h6  G                         T   W   W                           ,Y  $Y  X  Y  :  H  
         __sig__4 ;  ;  ;  I            X   Y              <  J           The intersection number (C,D)   $?  K                         X   X                                     4Y  X  (Y  xC  L  
         __sig__5 D  E  <E  M            X  0Y              \G  O                         W   W                                 TY  DY  X  8Y  L  P  
         __sig__6 M  M  M  Q            X  @Y              P  R           IntersectionPoints  <Q  TQ  w  
         __sig__4     P  x            pQ  Q              l	                   R                                      L   True iff the defining polynomial of N is nondegenerate an all the faces of N                              b                                           (R  pQ  R  (    
         __sig__7   l                pQ  $R                        >   /usr/local/magma-2.5/package/AlgGeom/linearsystem/sub_linsys.m H        6   Return a random hypersurface from the linear system L.                             L                                V         T  LS  S  
              LS   T                  
         RandomElement                      S                                      6   Return a random hypersurface from the linear system L.  ,                           L                                V          T  LS  T      
      	   __sig__10   x                LS  T                  
         GeneralElement    	                 T                              
        :   /usr/local/magma-2.5/package/AlgGeom/linearsystem/linsys.m       .   :   /usr/local/magma-2.5/package/AlgGeom/linearsystem/linsys.m    
         ambient '  ((  x(    
         sections )  )  *    
         is_complete <,  \,             defining_base_points                                                                      complete_linear_system  p2                                                                          L                                    pT  ,T  dT  9             HackobjPrintLinSys  :  :                   hT                                                            L                                     T  ,T      0@     
         __sig__1 A  tA  A  !            ,T  T              `D  "           HackobjCoerceLinSys E  F  #                 |T                              $        +   The complete linear system of degree d on P L  L  %                             R                          L      T  T  ,T  T  P  &  
         __sig__2 Q  Q  Q  '            ,T  T              S                           L   L                                 b  S  LS  S        
         __sig__6      5            LS  S                         ,   The hypersurface common to all elements of L                                L                                V          S  LS  S  7  
         __sig__7       %              LS  S                  (  
         LinearSystem      )                 T                              *        H   A maximal linear system of degree d on P whose elements do not contain C      D  +                         X       R                    L      T  T  ,T  T    ,  
         __sig__3        -            ,T  T                .        >   The linear system on P whose sections are the polynomials in F    /                            R                          L          T  ,T  T    0  
         __sig__4        1            ,T  T              4  2        >   True iff x is a polynomial section of L or a hypersurface of L  `  3                         L                                          T  ,T  T    4  
         __sig__5      `  5            ,T  T              x  6  
         HackobjInLinSys `*  7                 T                              8        5   The ambient space containing the schemes comprising L   7  9                         L                                P      \  T  ,T  T  (8  :  
         __sig__6 8     <8  ;            ,T  T              T8  =                 T                              >        "   The polynomials used to generate L      F  ?                         L                                           U  ,T  T  N  @  
         __sig__7 N     N  A            ,T   U              N  B  
         Sections T     HT  F  
         __sig__8 T     G             coefficient_space   4J  XJ             base_points                        complete_coefficient_space  N  O    
      	   dimension   8P  PP                                                
      
   base_locus  S  T    
         BaseComponent 7                     S                                      <   Remove any common factors from the generating functions of L L                               L                                L        S  LS  S       
         __sig__8 P                     LS  S              ,R     
         __sig__9                    >   /usr/local/magma-2.5/package/AlgGeom/linearsystem/sub_linsys.m                          T   L                          L      HR  <R  0R      7  
         __sig__0       =              0R  8R                    
      	   Subsystem   >                       4R                                                      T   L                          L      XR  PR  0R            
         __sig__1    >  a7            0R  LR                   &      y   The linear subsystem of L of hypersurfaces vanishing at a point or sequence of points or single point with multiplicity m   [t6                                 T   L                    L      hR  `R  0R  TR  @    
         __sig__2 7                   0R  \R              7        V   The subsystem of L determined by the subspace V of the complete coefficient space of L  7                         t    L                          L      xR  pR  0R  dR       
         __sig__3 @  7                0R  lR              @          :   The subsystem of L whose sections are the polynomials in F                    
         ImageSystem                      V                                      4   /usr/local/magma-2.5/package/AlgGeom/curve/aff_crv.m                              R                          X      k  W  W  W                W  W              (          2   The union of C and D in their common ambient space     d                           X   X                          X          W  W  W                W  W                  
         __sig__3 rojPl            &   Create the place at the simple point x                                  X                           _           X  W  W      
         __sig__2                     W  W              4             HackobjCoerceCrvProjPl  L                   W                                      I   True iff the point x lies on S or the sequence of coordinates x lies in S      H                           X                                          X  W  X  `*              W  X              x*             HackobjInCrvProjPl     *                   X                                
         __sig__5 ojPl   8  	           Print curve C at level l 8     ,8  
                            X                                    0X  W  $X  C    
         __sig__4 C     C              W  ,X              C             HackobjPrintCrvProjPl    F                   (X                                      D   An affine patch of C centred at the point p and the embedding into C    N                           T   X                          W[          HX  W  <X  W              W  DX              ,W             CentredAffinePatch          
         singular_germs  U              V  V                        S   The linear system of hypersurfaces of degree d in the range of f which contain f(S)                                   V   \                    L          V  V  V        
         __sig__2    %                  V  V                             8s  z              $    V      Q     3                             !  "  #  $  %  &  '  (  )  *  +  ,  -  .  /  0  1  2  3  4    5  6  "  7  8  9  :  ;  <  =  >  ?  @  A  B  C  D  E  F  G  H     I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  2   5  ]  ^  _    `  E#           TpD L  x  F#                                               G#  "      i   Computes Tp on the subspace of degree 0 divisors in the Mestre module. p must be a prime between 2 and 7.   d  |  H#                             8                                      (  8s    !  I#  
      
   __sig__314  #  #  J#            8s  $              \$  K#           TpX t%  %  L#                                                c#  
      
   __sig__319 tor  X)  M#        6   Computes the Eisenstein factor of the Mestre module X.  `-  N#                         8                                 8           @  8s  4  P1  O#  
      
   __sig__315  X2  p2  P#            8s  <              <4  Q#           MestreEisensteinFactor  |5  R#                 8                              S#           Returns the monodromy weights.  :  T#                         8                                            X  8s  L  x=  U#  
      
   __sig__316  ?  (?  V#            8s  T              @  W#        6   Returns the basis for D of supersingular j-invariants.  D  X#                         8                                        Ѝ  h  8s  \  I  Y#  
      
   __sig__317   L  L  Z#            8s  d              M  [#           SupersingularBasis  O  O  \#                 `                              ]#        N   Returns the decomposition of X into Hecke stable submodules under T2,T3,T5,T7.  U  _#        
   __sig__318   W  lW  W  W    
         __sig__4       <K              W  W                             HackobjPrintCrvAffPl    @                   W                                      2   The number of geometric punctures of C at infinity  @  7                         W                                           W  W  W                 W  W                             IsFlex r ty         =   /usr/local/magma-2.5/package/AlgGeom/linearsystem/vs_linsys.m   j7                         L   L                          L      dS  \S  LS  PS                 LS  XS              <3          K   A complement in L to the space of sections which contain the hypersurface S ڇx6                             V   L                          L          lS  LS  `S      
         __sig__1 7                   LS  hS              +7        F   The linear system containing hypersurfaces belonging to both L1 and L2  7                           L   L                          L      c  |S  LS  pS        
         __sig__2    4=                  LS  xS                   
         Intersection                        tS                                      F   The linear system containing hypersurfaces belonging to both L1 and L2  <?                           L   L                          L      c  S  LS  S        
         __sig__3    ?                  LS  S                         (   True iff L1 is a linear subsystem of L2.                                  L   L                                     S  LS  S        
         __sig__4    @  7            LS  S                   
         IsSubsystem 7                     S                                      (   True iff L1 is a linear subsystem of L2.    @  7                         L   L                                 b  S  LS  S       
         __sig__5 @  7                LS  S              @          K   True iff L1 and L2 are equal subsystems of a common complete linear system.         }            ,T  U              $    
      	   __sig__83       #                                               #                                                               $  8s        #  
      
   __sig__326  |    #            8s                   #           SerreModPQTableNM       #                                               #        
   __sig__328 Connected     #        R   Returns True if and only if the subtori intersection graph of J_k(N) is connected.  4  L  #                                                                   <  8s  0  !  #  
      
   __sig__327  "  "  #            8s  8              $  #           IsIntersectionGraphConnected %  (&  #                 4                              #           Given an integer N (the conductor), a sequence [d1,...,dr] of degrees which define a mod N character eps, and a sequence [p1,p2,...,pn] of primes p such that a_p=0, this function computes the subspace ker(Tp1') meet ker(Tp2') ... meet ker(Tpn') of the space M_5(Gamma_1(N),eps;F5bar)^+. (Primes denote transpose.) The first argument returned is the subspace W, and the second is the space of modular symbols. The subspace W is a subspace of the dual and can be computed efficiently using FastTp. <  H<  `<  #                                                      t t           T  8s  H  0@  #            8s  P              A  #                 L                              #           Artin2 List #                                                               h  8s      L  #  
      
   __sig__329  M  0M  #            8s  d              hO  #           TableEigenvalueList P  P  #                 `                              #  
      
   __sig__330  T  T  ]                         L                                t           |U  ,T  pU  	  `           CoefficientSpace 
  d
  
  a                 tU                              j  
      	   __sig__15 tSpace   b        D   The space of coefficients of the complete linear system containing L     c                         L                                t           U  ,T  U    d  
      	   __sig__14   x    e            ,T  U              H                   U                                      F   The coefficient vector of f in the complete linear system containing L  	                               L                          u           V  ,T   V      
      	   __sig__20                   ,T  V                  
         CoefficientMap                     V                                      R   The polynomial on the ambient space of L defined by the coefficient space vector v  ,  D                           u    L                                     $V  ,T  V      
      	   __sig__21   P!  x!              ,T   V              "    
         PolynomialMap   #                   V                                      3   The generic multiplicity of hypersurfaces of L at p )  $)                           T   L                                 tc  <V  ,T  0V  -    
      	   __sig__22   /  /              ,T  8V              L1          :   /usr/local/magma-2.5/package/AlgGeom/linearsystem/pencil.m  x&(*        :   /usr/local/magma-2.5/package/AlgGeom/linearsystem/pencil.m  &(*           Print L at level l  9  9                              M                                    TV  DV  HV  <    
         __sig__0 =  =  =              DV  PV              ?             HackobjPrintPncl A  pA  A                   LV                                                            M                                     hV  DV      I    
         __sig__1 K  K  L              DV  dV              |M             HackobjCoercePncl   O  O                   `V                                      %   The pencil on P determined by f and g   T             __sig__2 U  XU  U  U  U  f           CompleteCoefficientSpace       g                 U                              h           The base scheme of L "  "  i                         L                                V          U  ,T  U  $&  k            ,T  U              |'  l           The base scheme of L )  )  m                         L                                V          U  ,T  U  /  n  
      	   __sig__16   40  l0  o            ,T  U              1  p        =   The points of the base locus of L if that is zero-dimensional   4  q                         L                                           U  ,T  U  9  r  
      	   __sig__17   |:  :  s            ,T  U              ;  t        ?   True iff the hypersurfaces of L have no common geometric points >  >  >  u                         L                                           U  ,T  U  B  v  
      	   __sig__18   D  D  w            ,T  U              ,G  x  
         IsBasePointFree H  y                 U                              z        ?   True iff the hypersurfaces of L have no common geometric points O  O  P  {                         L                                           U  ,T  U  S  |        	   __sig__19   U  0U  XU  U                                   R                    M          V  DV  tV                DV  |V              	          =   /usr/local/magma-2.5/package/AlgGeom/linearsystem/maplinsys.m  8        =   /usr/local/magma-2.5/package/AlgGeom/linearsystem/maplinsys.m  8        \   The map from the ambient space of L to some projective space determined by the sections of L   T                           L                                \      V  V  V  V  ,    
         __sig__0                   V  V              h    $      s   The map P - -> Q determined by L; P is the ambient space of L, Q is any projective space of the same dimension as L `#  x#                           L   R   R                    \          V  V  V  &    
         __sig__1 '  $(  t(              V  V              *          N   The linear system on the domain of f determined by the polynomials defining f.  |/                           \                                L          V  V  V  2    
         __sig__2 3  3  84              V  V              x5             HomoloidalSystem 7  7  t8                   V                                      @   /usr/local/magma-2.5/package/AlgGeom/linearsystem/image_linsys.m <  X5 8        @   /usr/local/magma-2.5/package/AlgGeom/linearsystem/image_linsys.m @  5 8        0   The subsystem of L of hypersurfaces containing S D  tD  D                           V   L                          L          V  V  V  H    
         __sig__0 K  K  K              V  V              ,M          B   The polynomials of degree d in the range of f which vanish on f(S)  P  P                               V   \                               V  V  V  T             __sig__1 U  U  V  (V  XV  Z'  "      n   Returns an echelon basis for the subspace of W-anti-invariant theta functions for the Brandt series matrix TM.  @	  \'  
      	   __sig__11   d
  
  ]'              p                ^'           AntiInvariantTheta      _'                 l                              `'        6   Returns an echelon basis for the kernel subspace of W.  ,  a'                                                                           b'  
      	   __sig__12   x    c'                              d'  
         ThetaKernel     e'                                               f'        *   /home/was/magma/Kohel/modular_isogenies.mg  :@g'        *   /home/was/magma/Kohel/modular_isogenies.mg  0;@h'         f   Returns the sequence of points on X specifying isogenies of the elliptic curve E0 over its base field.  +  i'                             |                                            /  j'  
         __sig__0 0  0  1  k'                            p2  l'  
         ModularPoints   3  m'                                               n'  $      q   Returns the image curve F and the kernel polynomial of the isogeny E -> F corresponding to the modular data X, P.   p;  ;  o'                                 |                     | o           ĝ      >  p'  
         __sig__1 @  H@  x@  q'                            B  z'  
         __sig__3 ums D  D  r'         _   Given the sequence of successive power sums, returns the sequence of successive symmetric sums. I  4J  XJ  s'                                                                     ԝ    ȝ  O  t'  
         __sig__2 P  8P  PP  u'              Н              Q  v'           PowerToSymmetricSums S  S  w'                 ̝                              {'                            8X  |'  
         VeluIsogeny Y  Y  g           ResIntersectionAtInfinity >2       h                 Y                              i        ;   The points of C in the complement of its first affine patch        j                         X                                           Y  dY  Y  '  l            dY  Y                  m           ResPointsAtInfinity      n                 Y                              o        <   /usr/local/magma-2.5/package/AlgGeom/curve/singularity_crv.m BpLp     .   <   /usr/local/magma-2.5/package/AlgGeom/curve/singularity_crv.m BpLq                         W                                       Y  Y  Y          r  
         __sig__0    +      s            Y  Y                 t           True iff C is reduced   ;4u                         X                                       <b  Y  Y  Y     v  
         __sig__1   L7    w            Y  Y                x                         W                                       Y  Y  Y          y  
         __sig__2      7z            Y  Y                 {  
         The genus of C 5    |                         X                                           Y  Y  Y    }  
         __sig__3 7       ~            Y  Y              +7                         W                                       Z  Z  Y           
         __sig__4   d5                Y   Z              >    
         GeometricGenus                      Y                                         The geometric genus of C    8?                               X                                           Z  Y  Z       
         __sig__5 ?                     Y  Z              ?             The arithmetic genus of C      ?                           X                                           ,Z  Y   Z        
         __sig__6    A                  Y  (Z                   
         ArithmeticGenus                     $Z                                         The Milnor number of C                              W                                           DZ  Y  8Z  M    
         __sig__7       @              Y  @Z                    
         MilnorNumber @  7                 <Z                                      ,   True iff the origin is a singular point of C    @                           W                                       dc  \Z  Y  PZ        
         __sig__8    @  7            Y  XZ                  '  
         __sig__9        '            d                   '        J   Subspace of V orthogonal to U with respect to the Euclidean inner product.     4  '                         t    t                           t             d      '  
      	   __sig__10        '            d                  '        '   /home/was/magma/Kohel/modular_curves.mg S	'        '   /home/was/magma/Kohel/modular_curves.mg S
'        4   Returns the value of f under the pth Hecke operator.       '                                                               4  $  (  4  '            $  0              L  '  
      
   HeckeImage     `  '                 ,                              '  "      i   Returns the Brandt module of weight one theta functions for the binary quadratic forms of discriminant D.      |  '                                                                   L  $  @  *  '  
         __sig__1 1     d1  '            $  H              7  '           BinaryBrandtTheta      8  '                 D                              '        4   Returns a basis of weight two cusp forms of level N.    \8  '                                                                  t  d  $  X  C  '  
         __sig__2 F      F  '            $  `              8F  '  
         ModularBasis    N  '                 \                              '        G   Returns a basis of weight two cusp forms of level N and precision prec. `T     W  '                                                                   |  $  p  W  '  
         __sig__3 _           
         codimension                  ideal                  The projective plane curve f = 0 ˸         
         __sig__0                    4   /usr/local/magma-2.5/package/AlgGeom/curve/aff_crv.m Tp\           geometric_genus 1  Tp\           singular_origin        <3             singular_subscheme  7               singular_points                     ConvToManinSymbol        #        =   Compute the dimension of the new subspace of S_k(Gamma_0(N)).   <	  #                                                                   d  8s  X  @  #  
      
   __sig__306    0  #            8s  `              h  #  
         DimensionSknew    #                 \                              #        =   Compute the dimension of the new subspace of S_k(Gamma_0(N)).     #                                                                   |  8s  p  x  #  
      
   __sig__307  p    #            8s  x              x!   #           DimensionSkG1new "  "  "  !#                 t                              "#         d   Compute lots of information about dimensions of modular forms at level N and weight between 2 and k. )  T)  ##                                                                    8s    .  $#  
      
   __sig__308  /  /  %#            8s                1  &#  
         DimensionAll 2  2  '#                                               (#        ?   Returns a supersingular j-invariant in characteristic p < 10^6. $9  <9  9  )#                                                          r             8s    ,<  *#  
      
   __sig__309  =  ,=  +#            8s                $?  ,#           FindSupersingularJ  @  @  -#                                               .#                         r                                            8s      H  /#  
      
   __sig__310  J  TK  0#            8s                L  2#                                               :#            8s                ];#           Mestre  Q  <#                                               =#        +   Returns the Mestre method of graphs module. W  W  W  X    
      	   Punctures     (                   W                                      5   /usr/local/magma-2.5/package/AlgGeom/curve/proj_crv.m d        5   /usr/local/magma-2.5/package/AlgGeom/curve/proj_crv.m d  
         patches c_genus h     
         jacobian_ideal  !             jacobian_matrix "   #  #    
         __sig__1 roup        
         singularities   %  &                         T   X                          W      f  X  XX  X    (            XX  X              	  )                         T   W   W                           X  X  XX        *  
         __sig__4   |    +            XX  X                ,  
      	   IsTangent       -                 X                              .        1   True iff C and D are nonsingular and tangent at p     @  /                         T   X   X                               X  XX  X    0  
         __sig__5       1            XX  X              !  2        =   /usr/local/magma-2.5/package/AlgGeom/curve/intersection_crv.m  hS                 <Y                              T        "   The intersection points of C and D  (  (  U                         X   X                                     \Y  X  PY  -  V  
         __sig__7 /  h/  /  W            X  XY              1  X        6   /usr/local/magma-2.5/package/AlgGeom/curve/resultant.m  hY        6   /usr/local/magma-2.5/package/AlgGeom/curve/resultant.m  hZ                         W   W                                 Y  pY  dY      :  [  
         __sig__0 ;  ;  ;  \            dY  lY               =  ]  
         ResIntersection >  ^                 hY                              _         e   A sequence containing the intersection points of C and D; an error if C and D have a common component    G  `                         X   X                                     Y  dY  |Y  PL  a  
         __sig__1 M  hM  M  b            dY  Y              O  k  
         __sig__3 Infinity   c        L   The common points of C and D in the complement of their first affine patches T  T  e  
         __sig__2 U  U  V  f            dY  Y              8X  PX  lX                   @X                                      8   /usr/local/magma-2.5/package/AlgGeom/curve/tangent_crv.m ,  `hm        8   /usr/local/magma-2.5/package/AlgGeom/curve/tangent_crv.m 0  hm                         T   W                          W      tX  dX  XX      3    
         __sig__0 4  4  5              XX  `X              7    
         TangentLine @9  9                   \X                                      4   The tangent line to C at p embedded as a plane curve =  0=                           T   X                          X          |X  XX  pX  (A    
         __sig__1 B  B  B              XX  xX              @E                            T   W                          W      X  X  XX      XJ  !  
         __sig__2 L  hL  L  "            XX  X              M  x'  ,         Returns the isogeny E0 -> E1 with kernel defined by psi0, such that the invariant differential on E0 pulls back to the invariant differential on E1. 
  
  y'                         o    |                                            0  }'                                               ~'            Returns the kth derivative of f.   (    '                             Q                           Q               \  '  
         __sig__4     ,  '                               '            Returns the kth derivative of f.   p    '                             o                           o               #  '  
         __sig__5 #  #  $  '                            %  '        M   Returns the derivative with respect to the fixed generator of the base field.   )  '                         o                                 o       ,  $      /  '  
         __sig__6 /  40  l0  '                             1  '           Returns the derivative of f. 3  h3  '                         Q                                 Q           4    (  `7  '  
         __sig__7 9  9  9  '              0              :  '                         o    |                           o           @        =  '  
         __sig__8 ?  X?  x?  '              <              $A  '                 8                              '                             |                           Q           T        H  '  
         __sig__9 K  K  K  '              P              ,M  '  
         PhiOmega N  N  O  '                 L                              '         e   Returns codomain E1 of the isogeny of Velu, defined with respect to the monic kernel polynomial psi0.   U  '  
      	   __sig__10   W  W  (           R Series n  #  
         TangentCone 4P  LP  $                 X                              %        4   The tangent cone to C at p embedded as a plane curve U  U  '  
         __sig__3 V  V  hW          ,   The line through the distinct points p and q                              T   T                          S          [  [  [  
              [  [                        8   /usr/local/magma-2.5/package/AlgGeom/curve/weierstrass.m   0v}        8   /usr/local/magma-2.5/package/AlgGeom/curve/weierstrass.m   v}           Flexes s t                           T   X                          X\|       [  [  [          
         __sig__0   \  |              [  [              x    
         WeierstrassForm                    [                                T      2  A projective curve W in Weierstrass form isomorphic to the (closure of the) nonsingular genus 1 curve C. The second return value is a map of the ambient projective space restricting to an isomorphism W -> C taking the flex at infinity to p. The third return value is an expression of W in the CurveEll type  .  /                           T   W                          W\|           [  [  [  <2    
         __sig__1 3  P3  h3              [  [              5    >         A curve W in Weierstrass form isomorphic to the nonsingular genus 1 curve C. The second return value is a translation of the ambient space restricting to an isomorphism W -> C taking the flex at infinity to the flex at p =  =                           T   X                          X\|           [  [  [  A    
         __sig__2 C  DD  \D              [  [              F             WeierstrassFormFlex G  G                   [                                
      
   polynomial          :         A curve W in Weierstrass form isomorphic to the nonsingular genus 1 curve C. The second return value is a map of the ambient space restricting to an isomorphism W -> C taking the flex at infinity to p U  U  U                           T   X                          X\          [  [  [  0Z             Flex         
      	   __sig__18   H  `              Y  [                                         T   W                                 4[  $[  Y      `    
      	   __sig__19   X  p              Y   [                                 [                                      +   True iff p is an ordinary double point of C                              T   X                                     <[  Y  0[      
      	   __sig__20   \  |              Y  8[              x                           T   W                                 X[  H[  Y      !    
      	   __sig__21    #  #              Y  D[              X$             IsCusp  %                   @[                                      -   True iff p is a nonordinary double point of C   +                           T   X                                     `[  Y  T[  /    
      	   __sig__22   0  1              Y  \[              l2          7   /usr/local/magma-2.5/package/AlgGeom/curve/blowup_crv.m         7   /usr/local/magma-2.5/package/AlgGeom/curve/blowup_crv.m         8   The two natural patches of the blowup of C at the origin ;  l;  ;                           W                                WW      [  x[  h[  l[  >    
         __sig__0 @  D@  t@              h[  t[              B             Blowup  \D                   p[                                      ?   The birational transform of C under the toric blowup given by M K  K  L                           D    W                          W            [  h[  [  O    
         __sig__1 P  P  P              h[  [              @R          7   /usr/local/magma-2.5/package/AlgGeom/curve/crv_common.m         7   /usr/local/magma-2.5/package/AlgGeom/curve/crv_common.m   
         __sig__0 Z  tZ  Z    
         Singularities 7                     hZ                                      G   A sequence of the singular points of C defined over the base field of C @  7                             X                                            Z  Y  |Z  @    
      	   __sig__10 7                   Y  Z              7                         W                                       Z  Z  Y           
      	   __sig__11   7                Y  Z              @    
         SingularPoints                      Z                                      G   A sequence of the singular points of C defined over the base field of C 7         
      	   __sig__12             
      	   __sig__13           d                         X   X                                     Y  dY  Y      
         __sig__3                   [  [                ;'                                                                      
  >'        Y   The theta series with character Chi of the lattice with Gram matrix M, to precision prec.       ?'                                                                      (  @'  
         __sig__6   l    A'                               B'        >   The derivative f' - k*E2*f/12 of the modular form of weight k.    C'                                                                          D'  
         __sig__7 !   "  "  E'                            x#  F'           ModularDerivative   $  $  G'                                               H'        2   Returns an echelon basis for the Eisenstein space.  *  *  I'                                                                     ,       |/  J'  
         __sig__8 0  0  0  K'              (              <2  L'  
         EisensteinSpace h3  M'                 $                              N'        ,   Returns an echelon basis for the cusp space. 9  9  O'                                                                     D    8  ,<  P'  
         __sig__9 <  =  ,=  Q'              @              $?  R'  
      	   CuspSpace   @  @  S'                 <                              T'  "      i   Returns an echelon basis for the subspace of W-invariant theta functions for the Brandt series matrix TM.   I  I  U'                                                                   \    P  N  V'  
      	   __sig__10   O  P  W'              X              TQ  X'  
         InvariantTheta  R  Y'                 T                              ['                                                                   t    h  Y             IsOriginSingular 
    (                   TZ                                                       W                                        Z  pZ  Y          
         __sig__9   (                Y  lZ                                         X                                           Z  Y  Z                Y  Z                        	   __sig__15 verExtension                             W                                       Z  Z  Y      "              Y  Z              $             HasSingularPointsOverExtension  $&                   Z                                      L   False iff all the singularities of C are defined over its current base field -  \-                           X                                           Z  Y  Z  L1    
      	   __sig__14   T2  l2              Y  Z              84                           T   W                                  Z  Z  Y      8              Y  Z              d:                   Z                                         True iff p is a flex of C   \=  t=                           T   X                                      Z  Y  Z  A    
      	   __sig__16   @C  xC              Y  Z              lE                           T   W                                 [   [  Y      TK    
      	   __sig__17   L  L              Y  Z              N    
         IsDoublePoint   P                   Z                                      !   True iff p is a double point of C   T  T                           T   X                                     [  Y  [  X  /           The ambient space containing S  `  0                         S                                P          \  8\  \  	  2            8\  \              `  3           The dimension of S      4                         S                                       g  \  8\  \  @  5  
         __sig__7       6            8\  \              T  7        )   The codimension of S in its ambient space   t    8                         S                                           \  8\  \  x  9  
         __sig__8   p    :            8\  \              x!  ;  
         Codimension "  "  <                 \                              =        2   True iff the ambient space of S is an affine space  &  &  >                         S                                            ]  8\  \   ,  ?  
         __sig__9 -  -  -  @            8\  \              /  A  
         IsAffineScheme  1  B                 \                              C        5   True iff the ambient space of S is a projective space   x5  D                         S                                           ]  8\  ]  d:  E  
      	   __sig__10   <;  T;  F            8\  ]              <  G           IsProjectiveScheme  =  =  H                 ]                              I           True iff S is a point   B  J                         S                                       _  0]  8\  $]  \G  K  
      	   __sig__11   H  I  L            8\  ,]              LL  M        *   True iff the ambient space of S is a plane  N  O  N                         S                                           @]  8\  4]  Q  O  
      	   __sig__12   S  T  P            8\  <]              U  Q  
         IsPlanar W  W  W  R                 8]                              U  
      	   __sig__13   L[  |[              WeierstrassFormNonFlex  `                   [                                      2   /usr/local/magma-2.5/package/AlgGeom/curve/duval.m  (        2   /usr/local/magma-2.5/package/AlgGeom/curve/duval.m  8(                         T   X                                 (\  \  \          
         __sig__0   H  t              \  \                           IsAnalyticallyIrreducible     <                   \                              	        %   True iff C has exactly one place at p     
                         T   W                                     0\  \  $\  "    
         __sig__1 #  #  #              \  ,\              %          1   /usr/local/magma-2.5/package/AlgGeom/scheme/sch.m   (     &   1   /usr/local/magma-2.5/package/AlgGeom/scheme/sch.m   (           dimension_procedure .  .  !  
         __sig__1          %  
         __sig__2                                                                                                                  >  
         __sig__1 l                )   The scheme defined by the function 1 on A   :  :                           P                                S          `\  8\  T\  t=    
         __sig__0 >  ?  $?              8\  \\              @  %  
         __sig__3 B  HB  B  &            8\  \              D  '           The base ring of S  G  ,G  (                         S                                      g  \  8\  \  |L  )  
         __sig__4 M  M  M  *            8\  \              O  +        0   The base ring of S iff S is defined over a field Q  Q  Q  ,                         S                                      f  \  8\  \  XV  -  
         __sig__5 X  X  4X  .            8\  \              0Z  1           __sig__6 [  L[  |[  [  [                           S                                           \^  ^  P^                ^  X^              	  '            $  x              (  &  
         __sig__5 eld   @   '        2   Returns the function field of the modular curve X.    0  !'                                                                      $    t  "'  
         __sig__4     t  #'            $                \  &                                                                    $    H  &            $                  %'                            x!  &'           EllipticCuspForm "  "  "  ''                                               ('        '   The cusp form of a minimal model for E. &  &  &  )'                             |                                            ,  +'                            -  ,'  
         CuspForm /  /  /  -'                                               .'        @   Returns the zeta function at p of the rational elliptic curve E. 4  4  4  /'                             |                                     Ĝ      9  0'  
         __sig__2 :  :  :  1'                            ;  <'  
         __sig__5 ynomial <  2'        J   Returns the characteristc polynomial of Frobenius on the elliptic curve E.  @  @  3'                         |                                       ܜ  Ԝ    Ȝ  lE  4'  
         __sig__3 G  DG  \G  5'              М              I  6'        X   Returns the characteristc polynomial of Frobenius at p on the rational elliptic curve E. O  $O  dO  7'                             |                                 `      ؜  @R  8'  
         __sig__4 T   T  tT  9'                            V  :'        E   The theta series of the lattice with Gram matrix M to precision prec.   0Z  ='                            [  '           PhiLog eta  S        *   True iff S is defined by a single equation      T                         S                                           X]  8\  L]  
  V            8\  T]              @  W  
         IsHypersurface  0  X                 P]                              Y        =   True iff Groebner basis calculations can be carried out for S     Z                         S                                       @g  p]  8\  d]    [  
      	   __sig__14   \  |  \            8\  l]              x  ]           HasGroebnerBasis       ^                 h]                              _        O   True iff factorisation and irreducibility calculations can be carried out for S H%  p%  %  `                         S                                       Pg  ]  8\  |]  T)  a  
      	   __sig__15   +  +  b            8\  ]              -  c           HasFactorisation /  /  /  d                 ]                              e        P   True iff factorisation and irreducibility calculations can be carried out for S  5  (5  H5  f                         S                                       `g  ]  8\  ]  4:  g  
      	   __sig__16   ;  $;  h            8\  ]              \<  i           HasFactorization =  =  =  j                 ]                              k        8   True iff resultant calculations can be carried out for S D  tD  D  l                         S                                       pg  ]  8\  ]  H  m  
      	   __sig__17   K  K  n            8\  ]              ,M  o  
         HasResultant N  O  p                 ]                              q        2   True iff GCD calculations can be carried out for S  S  T  r                         S                                       g  ]  8\  ]  4X  s  
      	   __sig__18   Y  Y  t            8\  ]              |[    
         EmptyScheme ;  ;                   X\                                      (   Assign names N to the ambient space of S @  D@  t@                            S                                f  x\  8\  l\  D    
         __sig__1 F  F  F              8\  t\              H          '   The i-th name of the ambient space of S |L  L  L                                S                                 f  \  8\  |\  |P  !  
         __sig__2 Q  Q  Q  "            8\  \              S  #        '   The i-th name of the ambient space of S V  (V  XV  $                             S                                 f  \  8\  \  Z    
         Equation                        T^                                                       U                                       x^  p^  ^      `    
         __sig__5   X  p              ^  l^                            The degree of the hypersurface S   (  @                           V                                       $n  ^  ^  t^  t    
         __sig__6                   ^  |^              ,             The coordinate ring of S                                S                                       h  ^  ^  ^  x!    
         __sig__7 "  "  "              ^  ^              #                           U                                       ^  ^  ^      '    
         __sig__8 (  )  $)              ^  ^              +             The jacobian ideal of S -  -  -                           V                                           ^  ^  ^  1    
         __sig__9 2  2  2              ^  ^              4                           U                                D       ^  ^  ^      9    
      	   __sig__10   |:  :              ^  ^              ;          B   The matrix of partial derivatives of the defining polynomials of S  >  >                           V                                D           ^  ^  ^  B    
      	   __sig__11   D  D              ^  ^              ,G                           U                                D       ^  ^  ^      |L    
      	   __sig__12   M  M              ^  ^              O    
         HessianMatrix   P                   ^                                      P   The matrix of second partial derivatives of the polynomial of the hypersurface S W  W  X                           V                                D           ^  ^  ^  [    
      	   __sig__13   t]  ]  I        2   /usr/local/magma-2.5/package/AlgGeom/scheme/type.m  J        %   The scheme S as an affine plane curve   p	  K                         U                                W          4a  $a  (a  t  L  
         __sig__0   L  d  M            $a  0a                N           AffinePlaneCurveType     O                 ,a                              P        (   The scheme S as a projective plane curve   x    Q                         V                                X          La  $a  @a  |  R  
         __sig__1   t    S            $a  Ha              |!  T           ProjectivePlaneCurveType "  #  #  U                 Da                              V        9   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_closure.m    W        9   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_closure.m   X           curve   e   X           The projective closure of S /   0  Y                         U                                V      |a  la  \a  `a  83  Z  
         __sig__0 4  4  4  [            \a  ha              l6  \           ProjectiveClosure    9  (9  ]                 da                              ^  (         A closure of the image of S under f whenever f is a standard chart up to a translation made by homogenising the equations individually  0@  _                         [   U                          V      j  a  \a  xa  D  `  
         __sig__1 F  F  F  a            \a  a              H  b  (         The intersection of the projective closure of S with the hyperplane at infinity in the projective closure of the ambient space of S O  O  c                         U                                V          a  \a  a  (S  d  
         __sig__2 T  T  T  e            \a  a              V  f           SchemeAtInfinity X  X  X  g                 a                              h        ,   The sequence of standard affine patches of S ]  ^  b           Weights               HessianDeterminant     <K                   ^                                                       V                                           _  ^      LO    
      	   __sig__15      @              ^  _                                           W                                       (_  _  ^           
      	   __sig__16                      ^  _              V             InflectionPoints @  7                     _                                         The points of inflexion of C    Y                           X                                           0_  ^  $_        
      	   __sig__17   4\                  ^  ,_                                           W                                       L_  <_  ^          
      	   __sig__18     	              ^  8_              
                   4_                                         The points of inflexion of C                              X                                           T_  ^  H_      
      	   __sig__19     $              ^  P_              t                           W                                T      p_  `_  ^          
      	   __sig__20                   ^  \_              h                    X_                                      #   One of the points of inflexion of C #  $                           X                                T          x_  ^  l_  |'    
      	   __sig__21   <)  T)              ^  t_               ,          0   /usr/local/magma-2.5/package/AlgGeom/scheme/pt.m /         *   0   /usr/local/magma-2.5/package/AlgGeom/scheme/pt.m 1  p   
         coordinates 3  43    
      	   equations   4  4                               P                          T      k  _  _  _  9              _  _              :             Origin  ;                                T                                     _  _      >    
         __sig__1 @  D@  t@              _  _              B    
         HackobjCoercePt D                   _                                                       T                                          _  _      |L    
         __sig__2 M  M  M              _  _              O    
         HackobjInPt P  P                   _                                         Print the point p at level l U  U                              T                                    _  _  _  Y    
         __sig__3 Z  [  ([              _  _              \]  u        :   /usr/local/magma-2.5/package/AlgGeom/scheme/hypersurface.m   v        :   /usr/local/magma-2.5/package/AlgGeom/scheme/hypersurface.m  xw        7   The hypersurface which is a common component of S and T        x                         S   S                                     ]  ]  ]    y  
         __sig__0     (  z            ]  ]              t              ^  ^              $                           U                                       _  ^  ^      	    
      	   __sig__14   
  
              ^  ^              D                           P                                           g  f  g                f  g              (             IsProjectiveSpace      @                   g                                      )   True iff f is in the coordinate ring of A                                    P                                     g  f  g      
      	   __sig__16                    f  g                           IsAmbientFunction                          g                                
      
   coord_ring nction           =   True iff f in is the function field (or coordinate ring) of A   `                              P                                     g  f  g      
      	   __sig__17      `              f  g              x             IsAmbientRationalFunction      h*                   g                                      6   /usr/local/magma-2.5/package/AlgGeom/ambient/amb_aff.m h         6   /usr/local/magma-2.5/package/AlgGeom/ambient/amb_aff.m h        
                                             $   An n-dimensional affine space over k    C                                                         Q      (h  h   h  h  F    
         __sig__0 F     (F               h  h              N    
         AffineSpace    N                   h                              	        &   An affine space with coordinate ring R  XT  
                                                          Q          0h   h  $h  W    
         __sig__1 \     P\               h  ,h              `d          !   The point of A with coordinates S   \   \             __sig__0 ]  ]  ]  ]  ^  {  
         CommonComponent   |                 ]                              }        M   True iff the hypersurfaces S and T do not have a common irreducible component      ~                         S   S                                      ^  ]  ]  #    
         __sig__1 $  $  $              ]  ]              &             NoCommonComponent   ((  x(                   ]                                      8   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_common.m /       ,   8   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_common.m 2  0                         U                                       $^  ^  ^      |5    
         __sig__0 7  7  d7              ^  ^              9             The defining ideal of S (;  @;  X;                           V                                       a  ,^  ^   ^  >    
         __sig__1 ?  @  0@              ^  (^              A          2   The equations on some ambient space which define S  XE  pE                           S                                       `  <^  ^  0^  XK    
         __sig__2 L  L  L              ^  8^              N          -   The defining polynomial of the hypersurface S   P                           S                                           L^  ^  @^  T    
         __sig__3 V  ,V  \V              ^  H^              lX          -   The defining polynomial of the hypersurface S   ,[    
         __sig__4 \  ]   ]    
         HackobjPrintPt                     _                                          The sequence of coordinates of p 	  	  8
                           T                                           _  _  _       
         __sig__4                   _  _              @                           T   S                                  `  _  _      t    
         __sig__5                   _  _              ,          $   True iff p is a point of the space A   H                            T   P                                 `  `  _  _  !    
         __sig__6 "  "  "              _  `              $    "      j   True iff C is a sequence of coordinates of a point on S; if so also return the corresponding ambient point  )  $)                               S                           T          `  _  `  -    
         __sig__7 /  /  /              _  `              L1    
         __sig__9 ion 2  l2          D   True iff C is the coordinates of a point of S after some base change 5  x5                               S                                     (`  _  `  d:  	  
         __sig__8 ;  <;  T;  
            _  $`              <             IsPointOverExtension =  =                    `                                         The origin of A B  HB  B                           Q                                T          @`  _  4`  \G              _  <`              I                   8`                                       a   The sequence of coordinate points (0,..,1,..0) together with (1,..1) whether affine or projective   <Q  TQ                           P                                           X`  _  L`  U    
      	   __sig__10   V  hW              _  T`              X             Simplex `Z                   P`                                
      	   __sig__11   `^  ^    
         __sig__4                   b  Hc                        '   True iff p is not a singular point of S 	  	  	                           T   S                                     \c  b  Pc      
         __sig__5                   b  Xc                        ,   True iff the origin is a singular point of S   x                           U                                           lc  b  `c  @    
         __sig__6   0  H              b  hc              L          @   The multiplicity of p as a point of S, where S is a hypersurface !  T!  |!                           T   S                                     |c  b  pc  \$    
         __sig__7 %  %  %              b  xc               '    
         __sig__9 rity   ()          E   True iff the tangent cone to S at p is reduced and S is singular at p   -                           T   S                                     c  b  c  1    
         __sig__8 2  2  2              b  c              l4             IsOrdinarySingularity   5                   c                                                       T                                S      c  c  b      0<              b  c              x=    
         SingularLocus   (?                   c                                                       U                                U      c  c  b      F    
      	   __sig__10   G  G              b  c              XK          L   The singular locus of S as an scheme embedded in the same ambient space as S O  hO                           V                                V        c  b  c  DR    
      	   __sig__11   $T  xT              b  c              V          L   The singular locus of S as an scheme embedded in the same ambient space as S Z  dZ                           S                                S          c  b  c  ^    
      	   __sig__12   H`  ``          :   The point whose coordinates are the negative of those of p  7                             T                                T          p`  _  d`  @              _  l`                             Minus                       h`                              ;           Scheme  es    "      g   The nonzero coordinates of p as a sequence together with a sequence of the indices of these coordinates    @  7                          T                                            `  _  |`     !  
      	   __sig__12   7    "            _  `              @  #           NonZeroCoordinates  4\      $                 `                              %        6   The indices of the zero coordinates of p as a sequence    &                         T                                           `  _  `  l	  '  
      	   __sig__13   
  
  (            _  `                )  
         ZeroCoordinates    *                 `                              +        6   Return a random integral point of the ambient space A.  (  ,                         P                                T          `  _  `    -  
      	   __sig__14   t    .            _  `                /  
         RandomPoint     0                 `                              1                        T                                       `  `  _      X$  2  
      	   __sig__15   %  %  3            _  `              '  4           Polynomials defining p  T)  5                         T                                           `  _  `  .  6  
      	   __sig__16   /  /  7            _  `              1  8                        T                                S      `  `  _      4  9  
      	   __sig__17    6  h6  :            _  `              $9  <                 `                              =        8   The reduced scheme supported on argument point or points <  =  ,=  >                         T                                S      td   a  _  `  $A  ?  
      	   __sig__18   B  B  @            _  `              <E  A                        T                                       a  a  _      TJ  B  
      	   __sig__19   dL  |L  C            _  a              M  D        >   The ideal defining the reduced scheme structure supported on p  $Q  E                         T                                           a  _  a  0U  F  
      	   __sig__20   lV  V  G            _  a              X  H        2   /usr/local/magma-2.5/package/AlgGeom/scheme/type.m  PM           HackobjInSchProj        N                 (e                              O        (   Print the projective scheme S at level l 
  
  
  P                            V                                    He  d  <e  `  Q  
         __sig__5   P  h  R            d  De                S           HackobjPrintSchProj H  t  T                 @e                              U           The affine cone of S     V                         V                                U      i  `e  d  Te  h  W  
         __sig__6       h   X            d  \e              !  Y  
      
   AffineCone   #  #  Z                 Xe                              [        5   /usr/local/magma-2.5/package/AlgGeom/scheme/support.m \        5   /usr/local/magma-2.5/package/AlgGeom/scheme/support.m ]                         T                                       e  |e  pe      /  ^  
         __sig__0 1  41  L1  _            pe  xe              2  `                         U                                       e  e  pe      h6  a  
         __sig__1 8  8  8  b            pe  e              d:  c        G   The sequence of ambient points which support S if it is a finite scheme <  <  <  d                         V                                       n  e  pe  e  @  e  
         __sig__2 B  HB  B  f            pe  e              D  g  "      j   A sequence of maps from affine spaces whose images partition P together with the additional point returned  K  L  h                         R                                 T          e  pe  e  O  i  
         __sig__3 P  P  P  j            pe  e              @R  w  
         __sig__0 nsion  tT  k                         U                                       e  e  pe      hX  l  
         __sig__4 Y  Z  0Z  m            pe  e              [  n           HasPointsOverExtension  ]  o                 e                              p        @   False iff the support of S is defined over the ground field of S d  d  d  *           HackobjCoerceSchAff H  `  +                 d                              ,        I   True iff the point x lies on S or the sequence of coordinates x lies in S       -                         U                                          d  Td  d  h  .  
         __sig__4   `    /            Td  d              (  0  
         HackobjInSchAff   1                 d                              2        $   Print the affine scheme S at level l     3                            U                                    d  Td  d     4  
         __sig__5 !  !  !  5            Td  d              H#  6           HackobjPrintSchAff  $  $  7                 d                              8        6   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_proj.m  "9        6   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_proj.m  ";           __sig__0 eterminant                                                                                                    :                             R                          V      d  d  d      8  <            d  d              d:  =                             R                          V      e  d  d      <  ?            d  d              >  @        F   The subscheme of the projective space P defined by the given functions  B  A                             R                          V          e  d   e  \G  B  
         __sig__2 H  H  I  C            d  e              LL  K  
         __sig__4 roj M  |M  D                              V                                     e  d      $Q  E  
         __sig__3 Q  R  @R  F            d  e              T  G           HackobjCoerceSchProj V  XV  H                 e                              I        I   True iff the point x lies on S or the sequence of coordinates x lies in S   D]  \]  J                         V                                          0e  d  $e  pa  L            d  ,e              c             RemoveHypersurface  @  7                 $d                                      *   The scheme S with any Z components removed     @                           S   S                          S          Dd  c  8d        
         __sig__4    @  7            c  @d                   
      
   Difference  7                     <d                                      5   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_aff.m %        5   /usr/local/magma-2.5/package/AlgGeom/scheme/sch_aff.m %           is_hypersurface        @             singular_locus             
         is_empty              
         __sig__2   X                b  b              	                           U                                       b  b  b          
         __sig__3                   b  b              4          G   True iff S is defined by the function 1 or by the trivial maximal ideal ,  L  x                           V                                           b  b  b  @    
         __sig__4   0  H              b  b              L             True iff S is contained in T                              S   S                                     b  b  b  L#    
         __sig__5 $  $$  \$              b  b              (&          9   /usr/local/magma-2.5/package/AlgGeom/scheme/singularity.m   @((.        9   /usr/local/magma-2.5/package/AlgGeom/scheme/singularity.m   ((.                         T                                       c   c  b      1    
         __sig__0 2  2  2              b  b              l4    
         IsNonSingular   |5                   b                                                       U                                       c  c  b       <    
         __sig__1 <  <   =              b  c              >          -   True iff S is nonsingular and equidimensional   A                           V                                       Tc  $c  b  c  F    
         __sig__2 G  G  G              b   c              XK          D   True iff S has at least one singular point or is not equidimensional N  O                           S                                       Dc  4c  b  (c   R    
         __sig__3 S  S  T              b  0c              U    
      
   IsSingular  W  W                   ,c                                          True iff p is a singularity of S \  h\  \                           T   S                                     Lc  b  @c  `  i                         V                                       j  a  \a  a    j  
         __sig__3 	  	  	  k            \a  a              d  l  
         AffinePatches   t  m                 a                              n        ,   The sequence of standard affine patches of S     o                         V                                       j  a  \a  a  x  p  
         __sig__4     @  q            \a  a                                         S                                           4b  $b  (b                $b  0b              	             True iff S is reduced   (                           S                                         Db  $b  8b      
         __sig__1                   $b  @b                        7   The support of the reducible part of the hypersurface S                                S                                           Tb  $b  Hb      
         __sig__2   `  x              $b  Pb                  
         ReducibleScheme x!                   Lb                                         True iff S is reducible $  $  $                           S                                           lb  $b  `b  (    
         __sig__3 *  *  *              $b  hb              ,    
         IsReducible .  /                   db                                          True iff the dimension of S is 0 2  2  2                           S                                           b  $b  xb  6    
         __sig__4 8  8  $9              $b  b              :          8   /usr/local/magma-2.5/package/AlgGeom/scheme/comparison.m <  59        8   /usr/local/magma-2.5/package/AlgGeom/scheme/comparison.m ?  69  
         __sig__1 pace   A          8   True iff the two arguments lie in the same ambient space E  TE  lE                           S   S                                     b  b  b  TK    
         __sig__0 L  L  L              b  b              N             IdenticalAmbientSpace   LP                   b                                      U   True iff S and T are defined by the same ideal of functions on the same ambient space   V                           S   S                                 g  b  b  b  Z              b  b              ]                           T                                       b  b  b      8a  r  
         AffineCharts     s                 a                              t        #   The i-th standard affine patch of S "  "  u                             V                          U      b  a  \a  a  $&  v  
         __sig__5 &  &  '  w            \a  a              T)  x  
         AffinePatch +  +  y                 a                              z        #   The i-th standard affine patch of S 0  0  {                             V                          U      b  a  \a  a  84  |  
         __sig__6 5  (5  H5  }            \a  a              `7  ~  
         AffineChart 9  9                   a                                      ]   A standard affine patch of S containing p, the point p in that chart and the chart map itself   $?                           T   V                          UT[      j  b  \a   b  xC    
         __sig__7 D  E  <E              \a  b              \G          ]   A standard affine patch of S containing p, the point p in that chart and the chart map itself   ,M                           T   V                          UT[      j  b  \a  b  P    
         __sig__8 Q  Q  Q              \a  b              tT          8   /usr/local/magma-2.5/package/AlgGeom/scheme/firstprops.m W  P?@     
   8   /usr/local/magma-2.5/package/AlgGeom/scheme/firstprops.m Z  ?@        =   True iff the hypersurface S is irreducible over its base ring   _    
         __sig__0 `  t`  `              b  c              $                           P                                           Hg  f  <g                f  Dg              (          N   True iff factorisation and irreducibility calculations can be carried out in A  t                           P                                           Xg  f  Lg                f  Tg                        N   True iff factorisation and irreducibility calculations can be carried out in A                             P                                           hg  f  \g      
      	   __sig__10      (              f  dg              @          7   True iff resultant calculations can be carried out in A h     l                           P                                           xg  f  lg  H    
      	   __sig__11      l              f  tg              T*          1   True iff GCD calculations can be carried out in A      *                           P                                           g  f  |g   8    
      	   __sig__12      8              f  g              ,8          ,   True iff A and B are the same ambient object    P8                           P   P                                 k  g  f  g  C    
      	   __sig__13      F              f  g              ,F             True iff A is an affine space   N                           P                                           g  f  g  @T    
      	   __sig__14      TT              f  g              W    
         IsAffineSpace   ,W                   g                                          True iff A is a projective space d     hd    
      	   __sig__15      Q                               Q                          U      d  |d  Td                                                                                                                                                                        
         __sig__0 `  `  `              Td  xd              b    
         SingularScheme                     c                                      ;   /usr/local/magma-2.5/package/AlgGeom/scheme/constructions.m JXS     
   ;   /usr/local/magma-2.5/package/AlgGeom/scheme/constructions.m JXS        >   The scheme defined by all of the defining equations of S and T                             S   S                          S          c  c  c      
         __sig__0   \  |              c  c              x          >   The scheme defined by all of the defining equations of S and T  x!                           S   S                          S          d  c  c  X$     
         __sig__1 %  %  %              c   d              '          .   The scheme S with its reduced scheme structure  *                           S                                S          d  c  d  |/    
         __sig__2 0  0  0              c  d              <2    
         ReducedScheme   h3                   d                                ,         The scheme S after removing any T components of it assuming that S and T are both hypersurfaces; the number of factors removed is also returned ;  <  ,<  	                         S   S                          S           ,d  c   d  ?  
  
         __sig__3 @   A  $A              c  (d              xC             hessian_determinant                  projective_closure_map       
         hessian_matrix  TK                                Q                          U      d  d  Td      dO  "            Td  d              P  #        B   The subscheme of the affine space A defined by the given functions   T  tT  $                             Q                          U      d  d  Td  d  hX  &            Td  d              `Z  '                              U                                     d  Td      ^  (  
         __sig__3 `  D`  \`  )            Td  d              a                           T   U                          U      $f  f  e          
         __sig__4 	  T	  l	              e  f              
          I   The tangent cone to S at p embedded as a scheme in the ambient space of S   x                             T   V                          V          ,f  e   f      
         __sig__5     $              e  (f              t          J   The tangent bundle of S together with the projection map of ambient spaces                               U                                U1          <f  e  0f       
         __sig__6 !   "  "              e  8f              x#    
         TangentBundle   $                   4f                                      1   The subscheme of S whose tangent spaces contain p   )  *                           T   U                          U1          Tf  e  Hf  L/    
         __sig__7 0  0  0              e  Pf              2    
      
   Tangencies  3  43                   Lf                                      *   True iff p lies on some tangent space of S  8  $9                           T   U                                     lf  e  `f  ;    
         __sig__8 <  <  <              e  hf              >    
      
   IsTangency  D@  t@                   df                                      6   /usr/local/magma-2.5/package/AlgGeom/scheme/pt_tests.m \        6   /usr/local/magma-2.5/package/AlgGeom/scheme/pt_tests.m \        '   True iff the points of S line on a line |M  M  M                          T                                           f  |f  f  TQ    
         __sig__0 R  R  R              |f  f              T    
         AreCollinear V  XV                   f                                      2   /usr/local/magma-2.5/package/AlgGeom/ambient/amb.m  [\     "   2   /usr/local/magma-2.5/package/AlgGeom/ambient/amb.m  [\  
      	   base_ring   `  8a  \           Grading roj   
         nr_of_coords d  Hd             IsCurve    q                         V                                           e  pe  e    r  
         __sig__5 	  	  	  s            pe  e              (  t        5   /usr/local/magma-2.5/package/AlgGeom/scheme/tangent.m hfu        5   /usr/local/magma-2.5/package/AlgGeom/scheme/tangent.m hfv                         T   T                          T      e  e  e      t  x            e  e              \  &                         t                                            d      &            d                (  &        "   Returns the eigenvalues of M on V.     H  &                         t                                           d      &  
         __sig__4        &            d                  '  
         __sig__0 ent      &        S   Space orthogonal to u with respect to the inner product given by the Gram matrix M.      &                         u                               t       ԛ  ě  d    ,  &  
         __sig__5      @  &            d                X  &           OrthogonalComplement    p  &                                               &         _   Space orthogonal to elements of S with respect to the inner product given by the Gram matrix M. T*     \*  &                        u                               t         ܛ  d  Л  *  &  
         __sig__6 1     7  &            d  ؛              8  &        S   Space orthogonal to U with respect to the inner product given by the Gram matrix M.    @8  &                         t                               t           d    C  &  
         __sig__7 C     C  &            d                F  &        J   Subspace of V orthogonal to u with respect to the Euclidean inner product.     N  &                         u    t                           t           d    HT  &  
         __sig__8 T     \T  &            d                 W   '        V   Subspace of V orthogonal to elements of S with respect to the Euclidean inner product.  _  '                        u    t                           t           d     f             function_field                                                                         calc_factorisation  Z  4Z    
         calc_resultant  [                                    
         calc_gcd _  D_  h_             Assign names N to A `  <a                            P                                    f  f  f  e  &        -   /home/was/magma/Kohel/hecke_decompositions.mg 8r&        -   /home/was/magma/Kohel/hecke_decompositions.mg 8r&        K   Returns the sequence of vector subspaces stabilized by the Hecke operators. X  p  &                                                                     ,         &  
         __sig__0       &              (              $  &           HeckeModuleDecomposition       &                 $                              &  *         Returns the sequence of one dimensional vector subspaces stabilized by the Hecke operators, priority given to the divisors of the level N.  !  !  &                                                                   D    8  $  &  
         __sig__1 &  <&  T&  &              @              '  &        [   Returns the sequence of one dimensional vector subspaces stabilized by the Hecke operators. -  -  &                                                                 @  T    H  1  &  
         __sig__2 2  2  2  &              P              h4  "%                                                                         $9  &           HeckeEllipticData   |:  :  &                                               &        '   /home/was/magma/Kohel/linear_algebra.mg 8r&        '   /home/was/magma/Kohel/linear_algebra.mg 8r&        &   An LLL reduced basis of the span of B.  xC  &                        9                                        |  t  d  h  G  &  
         __sig__0 I  0J  TJ  &            d  p              L  &        6   An LLL reduced basis of the sublattice generated by B.  O  &                                                                      d  x  $S  &  
         __sig__1 T  T  T  &            d                V  &  
         __sig__3 ynomial X  &        0   Returns the characteristic polynomial of T on V. [  L[  |[  &                         t                                      ̜    d    ,`  &  
         __sig__2 a  Pa  pa  &            d                c  &        )   Returns the minimal polynomial of T on V.   f  4g    
         calc_groebner       
         __sig__0                   f  f              h              The i-th name of A  !  !                               P                                     f  f  f  $    
         __sig__1 &  <&  T&              f  f              '             The i-th name of A  )  *                               P                                     f  f  f  L/    
         __sig__2 0  0  0              f  f              2          0   The base ring of A iff A is defined over a field                                     P                                      Hu  f  f  f   9    
         __sig__5 f  f             The base ring of A  <  ,<                           P                                          g  f  g  ?    
         __sig__4 @   A  $A              f  g              xC              f   g              lE             The dimension of A  tG  G                           P                                       }   g  f  g  L    
         __sig__6 M  M  N              f  g              LP          )   The number of coordinates of a point of A   R  @R                           P                                           0g  f  $g  V    
         __sig__7 X  LX  hX              f  ,g              `Z             NumberOfCoordinates  \  \                   (g                                      <   True iff Groebner basis calculations can be carried out in A a  Xb    
         __sig__8 d  0d  Hd    
         __sig__9 e  e  @f  y  
         TangentSpace E  F  z                 e                              {                         T   U                          U      e  e  e      M  |  
         __sig__1 O  O  O  }            e  e              P  ~        J   The tangent space to S at p embedded as a scheme in the ambient space of S  T  T                           T   V                          V          f  e  e  X    
         __sig__2 Z  tZ  Z              e   f              \                           T   T                          T      f  f  e      `    
         __sig__3 a  a  Xb              e  f              d  d  e  H           sign_decomposition_plus  ˸     K  
         is_canonical     I           sign_decomposition_minus      (  J  
         is_effective    <  M           normal_form 
        L  
         is_principal      ^                         X   ]                          ^      m  m  m  tm    _  
         __sig__3        `            m  |m                a        .   The prime divisor consisting of the place at p    b                         T   ]                          ^      m  m  m  m  $  c  
         __sig__4      8  d            m  m              P  e  (         The principal divisor (line through p,q) - (line at infinity) restricted to the curve together with the defining rational function     H  f                         T   T   ]                    ^           m  m  m  `*  g  
         __sig__5 *     t*  h            m  m              *  v  
         __sig__8 rveElt  1  i                              ^                                     m  m       8  j  
         __sig__6 8     48  k            m  m              L8  l           HackobjCoerceDivCurveElt C     C  m                 m                              n           Print d at level l     F  o                            ^                                    m  m  m  N  p  
         __sig__7 N     N  q            m  m              @T  r           HackobjPrintDivCurveElt XT  s                 m                              t           The divisor group containing d  W  u                         ^                                ]          m  m  m  pd  w            m  m              f  x           The prime factorisation of d    k  z  
         __sig__9 l     l  ~  
      	   __sig__10      8X             Print D at level l  Z  4Z                              ]                                    Xl  k  Ll  ^    
         __sig__3 _  _  0`              k  Tl              a  =&                                               >&  $      u   Returns the leading p coefficients of the nth division polynomial defining the kernel of the multiplication by n map.     ?&                                 |                     o             Ȗ    8  A&            Ȗ                 d  B&           PuiseuxDivisionPsi       C&                                               D&  $      r   Returns the function field element defining the numerator of the multiplication by n map on the x-coordinate of E.       E&                             |                           o             Ȗ      F&  
      	   __sig__27        G&            Ȗ                4  H&  
         DivisionPhi    H  I&                                               J&  $      r   Returns the function field element defining the numerator of the multiplication by n map on the y-coordinate of E.     h  K&                             |                           o           4  Ȗ  (  p*  L&  
      	   __sig__28      *  M&            Ȗ  0              l1  N&  
         DivisionOmega   7  O&                 ,                              P&        N   Returns the function field elements defining the multiplication by n map on E.  P8  Q&                             |                           o           L  Ȗ  @  C  R&  
      	   __sig__29      F  S&            Ȗ  H              ,F  T&           DivisionPolynomials    N  U&                 D                              h&  
      	   __sig__33 mial n T  V&        @   Returns the classical modular equation relating j(q) and j(q^N). W     W  W&                                                                 t  d  Ȗ  X  P\  X&  
      	   __sig__30      \d  Y&            Ȗ  `              f  Z&           ClassicalModularEquation h     h  ^&  
      	   __sig__31      I  H        '   True iff x is a point or subscheme of A   H     I                         R                                          ,i  h   i  
  K            h  (i                &        &   /home/was/magma/Kohel/modular_forms.mg &        '   The cusp form of a minimal model for E. Ȗ    &                                               &        A   Returns the j-invariant as an element of the function field of X. sical Eise&                                                                      $       &            $                    &        8   Returns the canonical involution of the modular curve X.     &           EisensteinFunction  $%  L%  &                                               &                                                                     К  $  ̚  &  
         __sig__8            &            $  Ԛ              Ȗ  &  6         Returns an integer representing the "genus type" of X, defined to be 0 if the genus of X is zero, and 1 if X is of genus one or hyperelliptic over the quotient by the canonical involution.        &                                                                       $  ܚ  8   &  
         __sig__9     &           CanonicalInvolution (>  >  &                 Ț                              &  *         Returns an element of the function field which disappears on the locus of points for which this model of the modular curve is singular. iptic over t&                                                                      $        &  
      	   __sig__10     Ȗ  &            $                P  &        	   __sig__11              R  &  
      	   GenusType   S  T  &                 ؚ                              &        %   Returns the modular curve of level N. ld whi&                                                                       $    `]  &            $                    &                             |                                           8$'  
         __sig__0        Pe  %              `              p(ʸ           The affine plane over k 5  $6  l6                                                           Q          @h   h  4h  :    
         __sig__2 ;  ;  ;               h  <h               =          !   The point of A with coordinates S   \?  |?                                Q                           T          Ph   h  Dh  `D    
         __sig__3 E  XE  pE               h  Lh              G             HackobjCoerceAmbAff 4J  XJ                   Hh                                      '   True iff x is a point or subscheme of A O   P   P                           Q                                          hh   h  \h  S    
         __sig__4 T  U  4U               h  dh              lW    
         HackobjInAmbAff X                   `h                                         Print A at level l  H]  `]                              Q                                    h   h  th  ta    
         __sig__5 b  c  <c                h  |h              Pe  [&                 \                              \&        G   Returns the classical modular equation over K relating j(q) and j(q^N). 	  	  8
  ]&                                                                  |  Ȗ  p     _&            Ȗ  x              0  `&        +   Returns the Hilbert class polynomial for D.     a&                                                                       Ȗ      b&  
      	   __sig__32   l    c&            Ȗ                  d&           HilbertClassPolynomial    e&                                               f&  $      u   Returns the sequence of reduced forms for the order of index m in the quadratic field of fundamental discriminant DK.   H%  g&                                                                     Ȗ    $)  i&            Ȗ                +  j&        4   Returns the inverse of f as a binary quadratic form. /  L/  k&                                                                       Ȗ    l2  l&  
      	   __sig__34   3  3  m&            Ȗ                H5  n&  
         FormInverse 6   7  o&                                               p&  ,         Returns the reduced binary quadratic forms in the kernel of the map of class groups from forms of discriminant m^2*DK to form of discriminant DK.   X?  x?  q&                                                                   ̙  Ȗ    \D  r&  
      	   __sig__35   TE  lE  s&            Ȗ  ș              G  t&  
         KernelForms I  I  u&                 ę                              v&        >   Returns the composite of the binary quadratic forms q1 and q2.  LP  w&                                                                     Ȗ  ؙ  T  x&  
      	   __sig__36   XU  U  y&            Ȗ                W  z&  
         FormComposite   X  {&                 ܙ                              |&        8   Returns the reduction of the quadratic form A = <a,b,c>. _  @_  d_  }&                                                                       Ȗ    c  ~&  
      	   __sig__37   4e  Le  &            Ȗ                g  &  
      	   __sig__38   pi  i                           Q                                R          j  i   j      
         __sig__3 ity 	  	          H   The hyperplane at infinity as a subscheme of the projective closure of A                                Q                                V          j  i  j      
         __sig__2   (                i  j                           HyperplaneAtInfinity                      j                                      >   The line at infinity as a curve in the projective closure of A                             Q                                X          4j  i  (j  "              i  0j              $    
         LineAtInfinity  %                   ,j                                      *   The sequence of standard affine patch maps  @+  +                           R                                           Lj  i  @j  /    
         __sig__4 0  0  1              i  Hj              l2    
         AffinePatchMaps 3                   Dj                                      *   The sequence of standard affine patch maps  9  9                           R                                           dj  i  Xj  \<    
         __sig__5 =  \=  t=              i  `j              x?                   j                                      @   The sequence of affine spaces that comprise the standard patches F  F  F                           R                                           j  i  j  L    
         __sig__8 L  M  ,M              i  j              dO          @   The sequence of affine spaces that comprise the standard patches Q  Q  Q                           R                                           j  i  j  XV    
         __sig__9 X  X  4X              i  j              0Z          #   The i-th standard affine patch of P d\  \                               R                          Q      j  j  i  j  `    
      	   __sig__10   a  Xb              i  j              d          #   The i-th standard affine patch of P g  g    
      	   __sig__11   pi  i  ]                 di                              ^        /   The sequence of weights on the coordinates of P 7       _                         R                                           i  h  xi  7`  
         __sig__9       \  a            h  i                  c                 |i                              d        '   False iff the grading on P is [1,1,...]    @  7e                         R                                           i  h  i     f  
      	   __sig__10   7    g            h  i              @  h  
      
   IsWeighted 7       i                 i                              j           The function field of P             !           HackobjPrintAmbAff       "                 xh                              #           The coordinate ring of A 	  	  8
  $                         Q                                       Ti  h   h  h     %  
         __sig__6       &             h  h              @  '           The function field of A     (  (                         Q                                P       i  h   h  h    )  
         __sig__7   t    *             h  h                +        7   /usr/local/magma-2.5/package/AlgGeom/ambient/amb_proj.m  ,        7   /usr/local/magma-2.5/package/AlgGeom/ambient/amb_proj.m  -  
         grading ng  #  $  .           affine_patch_maps   x /           affine_cone_map &  &  '  0        1   An n-dimensional projective space over the ring k   @+  +  1                                                       R      h  h  h  h  /  2  
         __sig__0 0  0  1  3            h  h              l2  &        ;   Returns the discriminant of the quadratic form q = <a,b,c>.     &                                                                       Ȗ     
  &            Ȗ                @  &         b   Returns the class number of the order of discriminant D in a quadratic extension of the rationals.  `    &                                                                       Ȗ      &  
      	   __sig__39   <  \  &            Ȗ                  &        1   Returns the points of the projective line over R.   0  h  &                         M                                            ,  Ȗ     X"  &  
      	   __sig__40   `#  x#  &            Ȗ  (              $  &  
         ProjectiveLine  T&  &                 $                              &        8   Returns the sequence of maximal prime powers dividing n. ,  ,  ,  &                                                                     D  Ȗ  8  1  &  
      	   __sig__41   $2  <2  &            Ȗ  @              3  &           PrimePowerDivisors  (5  H5  &                 <                              &           Returns the set of units in R.  :  &                         M                                           \  Ȗ  P  ,=  &  
      	   __sig__42   >  >  &            Ȗ  X              @  &                 T                              &  
         __sig__6  ld E  <E  &        )   Returns the level of the modular curve X. curve X.  &                                                                     p  $  l  Ȗ  &            $  t              O  &            $                P  &           ModularFunctionField R  @R  &                                               &  (         Returns the function field element giving the quotient of the classical Eisenstein series of weight k by a power of a fixed form on X.      &  
         __sig__7 ˸    Ȗ  &  
         ModularLevel _  ,`  &                 h                              &        &   /home/was/magma/Kohel/modular_forms.mg *'  
         __sig__1    g  g  &  
         ModularCurve i  Hi  L           HackobjInAmbProj   H  `  M                 $i                              N           Print P at level l  	  8
  O                            R                                    Di  h  8i     P  
         __sig__6       Q            h  @i              @  R           HackobjPrintAmbProj (    S                 <i                              T           The coordinate ring of P     <  U                         R                                           \i  h  Pi    V  
         __sig__7       W            h  Xi              !  X        '   The grading on the coordinate ring of P x#  #  #  Y                         R                                           li  h  `i  &  Z  
         __sig__8 (  (  (  [            h  hi              +  k                         R                                P           i  h  i  /  l  
      	   __sig__11   0  1  m            h  i              l2  n        6   The affine cone of P together with the projection to P  5  o                         R                                Q[          i  h  i  9  p  
      	   __sig__12   :  :  q            h  i              ,<  r        &   The map from the affine cone of P to P  =  s                         R                                [          i  h  i  B  t  
      	   __sig__13   tD  D  u            h  i              F  v  
         AffineConeMap   G  w                 i                              x        :   /usr/local/magma-2.5/package/AlgGeom/ambient/amb_closure.m  y        :   /usr/local/magma-2.5/package/AlgGeom/ambient/amb_closure.m  0  
         __sig__1 Map S  S  z        2   The inclusion map from A to its projective closure  lV  V  {                         Q                                [          i  i  i  Z  |  
         __sig__0 \  d\  \  }            i  i              ^  ~           ProjectiveClosureMap `  `                   i                                         The projective closure of A de  e              i  j              Th  4  
         ProjectiveSpace 4  5                 h                              6        5   A projective space with homogeneous coordinate ring R   :  7                                                          R      h  h  h  h  ,=  8  
         __sig__1 >  >  >  9            h  h              @  :        1   A weighted projective space over k with weights W   tD  D  ;                                                       R          h  h  h  H  <  
         __sig__2 K  K  K  =            h  h              ,M  >           The projective plane over k O  O  ?                                                         R          i  h  h  R  @  
         __sig__3 T  T  T  A            h   i              XV  J  
         __sig__5 roj X  4X  B        !   The point of P with coordinates S   tZ  Z  C                             R                           T          i  h  i  _  D  
         __sig__4 `  t`  `  E            h  i              Xb  F           HackobjCoerceAmbProj d  d  G                 i                                                           R                          Q      j  j  i  j                i  j              	          ]   A standard affine patch of P containing p, the point p in that chart and the chart map itself                               T   R                          QT[          j  i  j      
      	   __sig__12     (              i  j              t           `   A standard affine patch of P containing p, the image of p in that chart and the chart map itself                                T   R                          QT[          j  i  j       
      	   __sig__13    "  "              i  j              x#          5   /usr/local/magma-2.5/package/AlgGeom/divisors/place.m         5   /usr/local/magma-2.5/package/AlgGeom/divisors/place.m   
      	   is_simple   @+  +             projective_curve ,  -  \-             point   /    
                                 puiseux_expansion   1  1                           T   W                          _      8k  (k  k      5    
         __sig__0 6  6  6              k  $k              9    
         SimplePlace |:  :                    k                                         Create the simple place p on C  =                           T   X                          _          @k  k  4k  A    
         __sig__1 C  DD  \D              k  <k              F    
         __sig__4 rve    G                                _                                     Lk  k      L    
         __sig__2 M  M  N              k  Hk              LP             HackobjCoercePlcCurve   Q                   Dk                                         Print pl at level l U  V                              _                                    dk  k  Xk  `Z    
         __sig__3 [  [  [              k  `k              ]             HackobjPrintPlcCurve _  ,`                   \k                                      8   True iff pl is a place at a nonsingular point of a curve f  Xf  pf              k  xk              i             __sig__5 j  8j  Pj  hj  j  %        $   Returns the identity isogeny E -> E.     %                         |                                              Ȗ    <
  %  
      	   __sig__13   L  d  %            Ȗ                  %           EllipticIdentity       %                                               %        $   Returns the domain of the isogeny f.     %                                                          |             Ȗ       &  
      	   __sig__14   `    &            Ȗ                 |  &        &   Returns the codomain of the isogeny f.     &                                                          |             Ȗ    #  &  
      	   __sig__15   $  $  &            Ȗ                &  &  
      	   __sig__17 sm '  '  &        W   Returns the endomorphism of E defined by the function field elements phi, psi, and omg. `-  -  -  &                         o    o    o    |                          $  Ȗ    1  &  
      	   __sig__16   2  2  	&            Ȗ                 l4  
&           EllipticEndomorphism 5  5  &                                               &        :   Returns the pushforward of the kernel polynomial psi by f.  ;  ;  &                             o                           o           <  Ȗ  0  (?  &            Ȗ  8              @  &  
         PushForward LB  B  &                 4                              &        6   Returns the pullback of the kernel polynomial xi by f.  I  &                             o                           o           T  Ȗ  H  M  &  
      	   __sig__18   O  O  &            Ȗ  P              (Q  &  
         PullBack R  R  DR  &                 L                              &        6   Returns the Weierstrass p-series of E, to precision N.  lX  &                             |                                     l  Ȗ  `  \  &  
      	   __sig__19   ]  ^  &            Ȗ  h              ``  (&  
      	   __sig__22 ies   a  &  &      {   Returns the Tate model for the Weierstrass p-series, in terms of q = exp(2*pi*i*tau) and w = exp(2*pi*i*z), to precision N. h  i  &                                                            |  Ȗ  p  m  A  
         BestHyperplane    B                 l                              C        6   /usr/local/magma-2.5/package/AlgGeom/divisors/divelt.m D     H   6   /usr/local/magma-2.5/package/AlgGeom/divisors/divelt.m G  
         factorisation     &  
      	   __sig__20        &            Ȗ  x                 &           TateWeierstrassSeries      !&                 t                              "&  "      j   Returns the Tate model for the Weierstrass p-series, in terms of q = exp(2*pi*i*tau) and w to precision N.       #&                                                                Ȗ      $&  
      	   __sig__21        %&            Ȗ                  &&        ]   Returns the formal group power series x(z) of E, followed by the power series y(z) = -x(z)/z.   $  '&                             |                                       Ȗ    X  )&            Ȗ                p  *&  
         FormalGroup      +&                                               ,&        [   Returns the function field element defining the kernel of the multiplication by n map on E.    l*  -&                             |                           o             Ȗ    p1  .&  
      	   __sig__23       8  /&            Ȗ                8  0&  
         DivisionKernel  ,8  1&                                               2&  $      v   Returns the nth division polynomial, a function field element defining the kernel of the multiplication by n map on E.   F  3&                             |                           o           Ԙ  Ȗ  Ș  N  4&  
      	   __sig__24      N  5&            Ȗ  И              N  6&  
         DivisionPsi    HT  7&                 ̘                              @&  
      	   __sig__26 si    (W  8&  $      u   Returns the leading p coefficients of the nth division polynomial defining the kernel of the multiplication by n map.   ld  9&                                 |                     o             Ȗ    k  :&  
      	   __sig__25       l  ;&            Ȗ                m  <&           TruncatedDivisionPsi   
         AffineChartMaps PL                   \j                                      "   The i-th standard affine patch map  P  P                               R                          [          |j  i  pj  T    
         __sig__6 U  U  V              i  xj              8X    
         AffinePatchMap  Y                   tj                                      "   The i-th standard affine patch map   _   _                               R                                     j  i  j  <c    
         __sig__7 d  d   e              i  j              g    
         AffineChartMap  Li  y                         ^                                         m  m  m    {            m  m              	  |        !   The curve on which d is a divisor   x    }                         ^                                S      4p  m  m  m  0              m  m                           True iff d is the zero divisor  t                           ^                                           n  m   n  <    
      	   __sig__11   ,  D              m  n              H             True iff a is equal to b                                ^   ^                                 tp  n  m  n  H#    
      	   __sig__12    $  X$              m  n              $&    
         Degree of d &  '                           ^                                       q  ,n  m   n  X,    
      	   __sig__13   -  -              m  (n              /          .   True iff all coefficients of d are nonnegative  <2                           ^                                          <n  m  0n  x5    
      	   __sig__14   7  `7              m  8n              9    
         IsEffective :  :                   4n                                      3   Effective minimal divisors a,b satisfying d = a - b X?  x?                           ^                                ^^          Tn  m  Hn  \D    
      	   __sig__15   TE  lE              m  Pn              G             SignDecomposition   0J  TJ                   Ln                                         The sum of divisors a + b   O  O                           ^   ^                          ^      q  ln  m  `n  R    
      	   __sig__16   T  T              m  hn              XV             The inverse of d X  LX  hX                           ^                                ^      n  |n  m  pn  \    
      	   __sig__17   ]  ^              m  xn              \`              The difference of divisors a - b b  pb  b                           ^   ^                          ^      ,q  n  m  n  g    
      	   __sig__18   pi  i              m  n              hk    
      	   __sig__19   l  m  $           representative_divisor    %        &   The linear equivalence class of d in J    &                         ^   `                          a          p  p  p  H  '  
         __sig__0      t  (            p  p                6  
         __sig__3 rveElt    )                              a                                     p  p        *  
         __sig__1        +            p  p                >        (   The curve on which d is a jacobian point        ?                         a                                S          q  p  p  D  A            p   q              \  B  
         Degree of j    p  C                         a                                       q  q  p  q  \  D  
         __sig__6      p  E            p  q              \*  F           j + k   l*  G                         a   a                          a          $q  p  q  p1  H  
         __sig__7 7      8  I            p   q              8  J           -j     (8  K                         a                                a      <q  4q  p  (q  \8  L  
         __sig__8 C     C  M            p  0q              C  N           j - k   F  O                         a   a                          a          Dq  p  8q  N  P  
         __sig__9 N     N  Q            p  @q              N  R           n*j    HT  S                         a                              a          Tq  p  Hq  (W  T  
      	   __sig__10      W  U            p  Pq              _  X        J   The uniformizing element (an element with valuation 1) of the local ring L     f  Y                                                                 lr  lq  \q  `q  l  Z  
         __sig__0 m     m  [            \q  hq              4m             mlist       O           normal_form_rational_function     N           normal_form_divisor    @  S  
         __sig__0    
    P  
         linear_system       F             	     
                      Q        H   The divisor in the divisor group D given by the factorisation sequence S       @  R                            ]                          ^      Xm  Pm  m  Dm      T            m  Lm                 U        ,   The divisor in D of the ambient polynomial f    @  V                             ]                          ^      hm  `m  m  Tm      W  
         __sig__1    @  7X            m  \m                 Y        5   The divisor in D of the ambient rational polynomial f       Z                             ]                          ^      xm  pm  m  dm     [  
         __sig__2 h         \            m  lm               k  ]           The divisor in D of the line L        
         ProjectiveCurve                    k                                         The point underlying pl 	  	  	                           _                                T          k  k  k      
         __sig__7                   k  k                           The point underlying pl   (                             _                                T      4o  k  k  k  \    
         __sig__8     ,              k  k                  
         UnderlyingPoint h                   k                                         True iff pl is a place of C "  "                           _   S                                     k  k  k  $&    
         __sig__9 &  &  '              k  k              T)                   k                                      5   True iff p and q are the same place on the same curve   /                           _   _                                 l  k  k  k  43    
      	   __sig__10   4  4              k  k              h6          3   /usr/local/magma-2.5/package/AlgGeom/divisors/div.m 8P        3   /usr/local/magma-2.5/package/AlgGeom/divisors/div.m P   
         affine_model =  ,=    
         affine_curve >  >  E           group                 zero ctive_c  
         __sig__0                  has_normal_forms D  E  <E             best_hyperplane ,G  DG  \G                                                       W                                ]      (l   l  k      N              k  l              LP  	           The divisor group of C  Q  
                         X                                ]          0l  k  $l  U    
         __sig__1 W  W  W              k  ,l              tY    
         __sig__4 rve    Z          3   Consider the nonsingular point x as a prime divisor ]  ^                                ]                           ^          @l  k  4l  Xb    
         __sig__2 d  0d  Hd              k  <l              pf             HackobjCoerceDivCurve   i                   8l                                                       _                                           |k  k  pk                  The curve of which pl is a place                                     _                                S      l  k  k  k                  k  k                          +   The projective model of which pl is a place                                  _                                X      l  k  k  k        
         __sig__6                        k  k                             HackobjPrintDivCurve                       Pl                                      ,   True iff D was created using an affine curve 
  
                           ]                                           pl  k  dl  `              k  ll                  
         FromAffineCurve                    hl                                      &   The curve containing the elements of D                              ]                                S      m  l  k  |l    !  
         __sig__5       "            k  l                 #           The affine model underlying D   "  $                         ]                                W      Dp  l  k  l  %  %  
         __sig__6 &  &  &  &            k  l              $)  '  
         AffineCurve @+  +  (                 l                              )        1   The projective curve containing the elements of D   0  1  *                         ]                                X      Tp  l  k  l  h4  +  
         __sig__7 5  `5  x5  ,            k  l              t8  -           The zero divisor 9  9  4:  .                         ]                                ^      dp  l  k  l  <  /  
         __sig__8 =  =  =  0            k  l              ,@  1  
         ZeroDivisor pA  A  2                 l                              3           True iff D is equal to E F  G  ,G  4                         ]   ]                                 n  l  k  l  |L  5  
         __sig__9 M  M  M  6            k  l              O  7        A   True iff D is associated to a cubic curve with a flex at infinity   R  R  8                         ]                                 ^          l  k  l  hW  9  
      	   __sig__10   X  X  :            k  l              Z  ;  
         HasNormalForms  \  <                 l                              =        6   A good choice of divisor corresponding to a hyperplane  a  >                         ]                                ^           m  k  l  4g  ?  
      	   __sig__11   h  i  @            k  l              j             Omit ces    4#  
         ssbasis        5#  
         weights      !  3#           2   5  ]  ^  _    `  7#           eisen "8#                                                          8           8s      L  9#  
      
   __sig__311  U  V                                                                 `t  8s  Tt      
         __sig__0                4 8s  \t  X   x                      ManinSymbolApply                         Xt                                d      p  Apply an element g=[a,b, c,d] of SL(2,Z) to the given modular symbol. The definition of the action is g.(X^i*Y^j{u,v}) := (dX-bY)^i*(-cX+aY)^j {g(u),g(v)}. A modular symbol is represented as a pair <P,x>, where P is a polynomial in X and Y (an element of the ring M`mlist`R, and x=[[a,b],[c,d]] is a pair of elements of P^1(Q), where [a,b] <--> a/b and [c,d] <--> c/d. *     l*                                   t                            t  xt  8s  lt  p1    
         __sig__1 7      8          4 8s  tt  X            8             ModularSymbolApply     08                    pt                              !  f      }  Apply an element g=[a,b, c,d] of SL(2,Z) to the given modular symbol. The definition of the action is g.(X^i*Y^j{u,v}) := (dX-bY)^i*(-cX+aY)^j {g(u),g(v)}. A modular symbol is represented as a sequence of pairs <P,x>, where P is a polynomial in X and Y (an element of the ring M`mlist`R, and x=[[a,b],[c,d]] is a pair of elements of P^1(Q), where [a,b] <--> a/b and [c,d] <--> c/d.   \T  "                                 t                                t  8s  t  W  #  
         __sig__2 \     _  $        4 8s  t  X            dd  %        [   Returns the space of modular symbols of weight 2 for Gamma_0(N), over the rational numbers.    k  &                                                          t       t  t  8s  t  $m  '  
         __sig__3 m     8m  (            8s  t              Ds                                                               r  r  \q  q      
         __sig__8 	  X	  p	              \q   r              
          3   The unramified local ring with prime p and degree f                                                                    r  r  \q  r      
         __sig__9     ,              \q  r              x          @   The unramified local ring with prime p, degree f and precision n   x                                                                 ,r  $r  \q  r      
      	   __sig__10   !  <!              \q   r              "          S   The totally ramified local ring with prime p defined by the Eisenstein polynomial g %  (&                                                                 <r  4r  \q  (r  *    
      	   __sig__11   <,  \,              \q  0r               .           c   The totally ramified local ring with prime p and precision n defined by the Eisenstein polynomial g 2  2                                                               Lr  Dr  \q  8r  l6    
      	   __sig__12   8  8              \q  @r              h:          W   The local ring with prime p and inertia degree f defined by the Eisenstein polynomial g 0=  `=  x=                                                               \r  Tr  \q  Hr  A    
      	   __sig__13   DC  |C              \q  Pr              pE           d   The local ring with prime p, inertia degree f and precision n defined by the Eisenstein polynomial g L  PL                                                                 dr  \q  Xr   P    
      	   __sig__14   Q  (Q              \q  `r              R          J   The uniformizing element (an element with valuation 1) of the local ring L   W  lW                                                                       tr  \q  hr  ,[    
      	   __sig__15   ]   ]              \q  pr               _    *         The known part of the local element x. Note that this function will be removed in the next release; Expand() should be used in its place.   e  Df                                                                       r  \q  xr  j    
      	   __sig__16   `l  xl              \q  r              To             eps 3      ,           HackobjCoerceJacCurveElt       @V  -                 p                              .           Print j at level l     W  /                            a                                    p  p  p      0  
         __sig__2    d[      1            p  p                 2           HackobjPrintJacCurveElt 73                 p                              4           The jacobian containing j 7       5                         a                                `          p  p  p  77            p  p                 @  
         __sig__5 isor 7    8           A divisor in the class of j 7    9                         a                                ^          p  p  p  @  :  
         __sig__4 7       ;            p  p              7<           RepresentativeDivisor      =                 p                                              J   The underlying point in the projective plane of the single place divisor d                               ^                                T          <o  m  0o  `              m  8o                        1   The sequence of points underlying the places of d                                ^                                           Lo  m  @o  $    
      	   __sig__29                   m  Ho              <             UnderlyingPoints   \  |                   Do                                      E   The sequence of points forming the support of the effective divisor d   "                           ^                                           do  m  Xo  H%    
      	   __sig__30   l&  &              m  `o              t(    
         SupportPoints   *                   \o                                $      v   A divisor linearly equivalent to d but in a normal form (only in the case that the curve is a nonsingular plane cubic)  l2                           ^                                ^          |o  m  po  5    
      	   __sig__31   7  t8              m  xo              4:          #   Degree 1 divisor corresponding to d ;  ;                           ^                                ^          o  m  o  $?    
      	   __sig__32   @  @              m  o              B             NormalFormDivisor   D  D                   o                                
      	   __sig__34 Function          [   A rational function on projective plane whose divisor plus the normal form of d is d itself $O  dO                           ^                                           o  m  o  @R    
      	   __sig__33    T  tT              m  o              V             NormalFormRationalFunction  LX  hX                   o                                      Z   True iff d is a principal divisor in which case also return a rational function defining d  _  ,`                           ^                                           o  m  o  Hd              m  o              pf    
                               e   True iff d and e are linearly equivalent in which case also return a rational function defining d - e   Xn             The divisor n*d    H  `                           ^                              ^      Lq  n  m  n  	              m  n              `          :   The sum of the norms of the finite place coefficients of d  x                             ^                                       L  n  m  n      
      	   __sig__20     $              m  n              t          E   The sequence of places forming the support of the effective divisor d                              ^                                           n  m  n       
      	   __sig__21   !  !              m  n              H#          =   The underlying place of the divisor d based on a single point   $&                           ^                                T          n  m  n  *    
      	   __sig__22   8,  X,              m  n              .    
         UnderlyingPlace /                   n                                      F   The sequence of places appearing in the factorisation of the divisor d  5                           ^                                           n  m  n  9    
      	   __sig__23   :  :              m  n              ,<             UnderlyingPlaces =  \=  t=                   n                                                       _   ^                          ^       o  n  m      D    
      	   __sig__24   F  F              m  n              H          "   The component of d associated to p  4L  LL                           T   ^                          ^          o  m  n  P    
      	   __sig__25   Q  $Q              m  o              R                           _   ^                          ^      $o  o  m      hW    
      	   __sig__26   X  X              m  o              Z  %                 ,                              %                             |                                      L  Ȗ  @  <
  %  
         __sig__5   L  d  %            Ȗ  H                %        6   Returns true if P satisfies the equation of the curve.    %                         ~    |                                  l  \  Ȗ  P  (  %  
         __sig__6        %            Ȗ  X              @  %  
      	   IsOnCurve   0  H  %                 T                              %        6   Returns true if P satisfies the equation of the curve.  |!  %                             |                                      t  Ȗ  h  \$  %  
         __sig__7 %  %  %  %            Ȗ  p               '  %        @   Returns the value of the defining equation of E, evaluated at P. +  ,  $,  %                         ~    |                                      Ȗ  x  p0  %  
         __sig__8 1  1  1  %            Ȗ                2  %           EquationEvaluation  4  4  %                 |                              %        @   Returns the value of the defining equation of E, evaluated at P. :  :  :  %                             |                                        Ȗ    =  %  
         __sig__9 ?  \?  |?  %            Ȗ                (A  %        0   Returns the value of f evaluated at the point P. D  D  D  %                         ~    o                                     Ȗ    I  %  
      	   __sig__10   8L  PL  %            Ȗ                M  %           FunctionEvaluation  O  O  %                                               %        0   Returns the value of f evaluated at the point P. T  T  T  %                             o                                     ė  Ȗ    X  %  
      	   __sig__11   xZ  Z  %            Ȗ                \  %        Y   Returns the isogeny E0 -> E1 defined by the function field elements phi0, psi0, and omg0.   Ta  ta  %                         o    o    o    |    |                    ԗ  Ȗ  ȗ  Df  %  
      	   __sig__12    h  Xh  %            Ȗ  З              $j  %  
         EllipticIsogeny k  %                 ̗                                               o                                      E   The divisor d with all occurances of p removed from its factorisation   a                           T   ^                          ^          ,o  m   o  8g    
      	   __sig__27   h  i              m  (o              j  #                           	   __sig__28   Dn  \n  n  n              o  hp              $             True iff J is equal to I                                `   `                                     |p  o  pp  d    
         __sig__8   \  t              o  xp                         6   /usr/local/magma-2.5/package/AlgGeom/divisors/jacelt.m a!        6   /usr/local/magma-2.5/package/AlgGeom/divisors/jacelt.m a"  
         jacobian lt     %                                                                   ̔      %            ̔                  %        )   /home/was/magma/Kohel/elliptic_schemes.mg   Ya%     V   )   /home/was/magma/Kohel/elliptic_schemes.mg   0Za%        "   Elliptic scheme construction of E. %  %  %                         |                                 |         ܖ  Ȗ  Ж  )  %  
         __sig__0 +  ,  $,  %            Ȗ  ؖ              -  %  
         EllipticScheme  /  %                 Ԗ                              %  "      l   Returns the elliptic curve E with coefficients given by the sequence S, and assigns the function field of E. 6  l6  %                                                          |             Ȗ    :  %  
         __sig__1 ;  ;  ;  %            Ȗ                 =  %  
         __sig__3 ield   >  %        <   Returns the function field of E, followed by the y function. A  A  %                         |                                 n o             Ȗ     G  %  
         __sig__2 G   H  H  %            Ȗ                 K  %           EllipticFunctionField   0M  %                                               %  (         Returns a simplified Weierstrass model E1 of the elliptic curve E0, followed by the isomorphisms E0 -> E1 and E1 -> E0 between them. U  U  %                         |                                               Ȗ    Y  %            Ȗ                [  %           WeierstrassModel ]  x]  ]  %                                               %           The base extension of E to S.   \b  %                            |                           |           4  Ȗ  (  g  %  
         __sig__4 i  4i  Li  %            Ȗ  0              0k  %  
         BaseExtension   l  %           The trace of E at p. o  o  o  o                           ^   ^                                     o  m  o      
      	   __sig__35   	  	              m  o              d             AreLinearlyEquivalent                      o                                      3   /usr/local/magma-2.5/package/AlgGeom/divisors/jac.m c8l        3   /usr/local/magma-2.5/package/AlgGeom/divisors/jac.m Xc8l                         W                                `      o  o  o          
         __sig__0   d  |              o  o                           The jacobian of C   !  !                           X                                `      p  o  o  o  $    
         __sig__1 %  %  (&              o  o              '    
         __sig__4 rve    X)           I   Consider the nonsingular point p as an element of the jacobian of a curve   .   .                           T   `                           a          p  o   p  2    
         __sig__2 2   3  83              o  p              4          &   The degree f unramified extension of L                                                                   r  r  \q  r  8
    
      	   __sig__17   H  `              \q  r                %                                                                     (  ̔    @  %            ̔  $                %                         u    u                                    4  ̔      \  %            ̔  0                %  
      
   IsLessThan      %                 ,                              %                        u                                            H  ̔      #  %  
      	   __sig__20   #  $  %            ̔  D              %  %                 @                              %        7   Returns the lattice of the r-th externion power module.  ,  8,  X,  %                                                                   `  ̔  T  0  %  
      	   __sig__21   1  1  %            ̔  \              43  %  
         ExteriorModule  4  %                 X                              %        \   Returns the exterior product of v with the (r-1)-th exterior power module of L as a lattice. ;  ;  %                                                                 x  ̔  l  >  %  
      	   __sig__22   D@  t@  %            ̔  t              B  %  
         ExteriorProduct D  %                 p                              %  (         Given a matrix giving a homomorphism V -> W, returns the matrix giving the induced homomorphism of r-th exterior powers of V and W. M  N  %                             D                           D             ̔    Q  %  
      	   __sig__23   S  S  %            ̔                U  %  
         ExteriorMap V  hW  %                                               %        6   Returns the submatrix of coordinates (i,j) in I1 x I2.  ]  %                                 D                     D           ̔    8a  %  
      	   __sig__24   pb  b  %            ̔                e  %  
         MatrixMinor f  4g  %                                               %        6   Returns the submatrix of coordinates (i,j) in I1 x I2.  m  %  
      	   __sig__25   ho  o             HackobjCoerceJacCurve   `7                   p                                         Print J at level l  l;  ;                              `                                    $p  o  p  >    
         __sig__3 @  D@  t@  	            o   p              B  
           HackobjPrintJacCurve D  D                   p                                      &   The curve containing the elements of J  TK                           `                                S      p  <p  o  0p  dO              o  8p              P             The affine model underlying J   @R                           `                                W          Lp  o  @p  V    
         __sig__5 X  LX  hX              o  Hp              `Z          1   The projective curve containing the elements of J   t]  ]                           `                                X          \p  o  Pp  a    
         __sig__6 c  c  c              o  Xp              e              The zero divisor in the jacobian h  h  i                           `                                a          lp  o  `p  m             __sig__7 o  ho  o  o  o  $  &      }   Returns the sequences of sequences of Brandt modules of level N*M, for an order in the algebra ramified at primes dividing N.      $                                                               x  p  H  d  4?  $  
         __sig__1       >  $            H  l                  $  $      s   Returns the sequence of sequences of Brandt modules for the quaternion order defined by QuaternionAlgebra(D1,D2,T).        $                                                                 H  t  L@  $  
         __sig__2       @  $            H  |                  $        P   Returns the sequences of sequences of Brandt modules for the quaternion order A.    E      $                                                                       H       $  
         __sig__3 K         $            H                M  $        <   Returns the Brandt matrix of theta functions to precision N. P      $                                                                     H       $  
         __sig__4 S         $            H                @V  $  
         BrandtTheta    @  $                                               $        4   Returns the Gram matrix of the inner product for TM. @  7$                                                                       H       $  
         __sig__5 @  7    $            H                @  $           BrandtGramMatrix    ^      $                                               $        -   Returns the matrix of pth coefficients of TM.   b  $                                                                   Г  H  ē      $  
         __sig__6    le      $            H  ̓                 $  
         BrandtHecke        $                 ȓ                              $        U   Returns the Atkin-Lehner operator matrix for the Brandt module BM of quadratic forms.   7$                                                                       H  ܓ     $  
         __sig__7 s  #g8    $  
         AtkinLehner                   /home/was/magma/Hecke/hecke.m   
         theCategory   +7  
         disc             
         gammaalp                   Z         
      
   semidecomp                  SkF 3                 SkZ       
         ModSymBasis    l    
         BoundaryMap                 old 3                 sknew       
      	   sknewdual   &  '    
         SkZplus          
         SkZminus          
      	   mknewdual         
         newforms      !    
         oldforms   *  +             mknew       
         T_images                   X                  mestre  '             M   .  /    
         winding h     l             V eCategory            Zdual                qexp   %             eigen   -    
         cusplist (     T*    
      
   eigenminus        
         eigenint      !             moddeg  )    
         PeriodLattice   3             cinf   9    
      	   eigenplus      8    
         cinfimag                   Lvals                LRatio  '     
      	   LRatioOdd   0  1             cp  "  7             wq  >  ?    
      
   realvolume     C    
      
   imagvolume      F             iso 3                 isnew                iscusp  %             fast   -    
      	   signspace   5  6  	           xdata   =  
  
         ZxZalp  E  F  G    
      	   qintbasis      W    
         RatPeriodConj                RatPeriodMapSign   "  #    
      	   PeriodMap   ,  -             PeriodMapPrecision  "  7  K           Level  ply              Apply g to the ith Manin symbol.   M  N  O  P    
         VolLEven l     l    
         VolLOdd m     m    
      
   PeriodGens     0m             PGfast  @m    
         RatPeriodMap    Hs             RatPeriodLat    \s      k             decomp                discQ         
      	   newdecomp         
      	   olddecomp           ^        4   The generator of the maximal unramified subring of L     _                                                                     q  \q  xq    `  
         __sig__1       a            \q  q                                                                               ,s  \q   s               /home/was/magma/Hecke/hecke.m G        3   Return the level of the space M of modular symbols. ,  D  H                         t                                            (u  8s  u    I  
      	   __sig__11       J        4 8s  $u  X              d%        1   Returns the sequence of subsequences of length r.   @  `  e%                                                                     ̔    L  g%            ̔                  h%        1   Returns the sequence of subsequences of length r.   4"  \"  i%                                                                     ̔    %  j%  
      	   __sig__11   &  &  k%            ̔                (  l%                                                                        ̔      -  m%  
      	   __sig__12   h/  /  n%            ̔                1  o%           The factorization of f. p2  2  2  p%                         Q                                        Е  ȕ  ̔    l6  q%  
      	   __sig__13   8  8  r%            ̔  ĕ              h:  s%        "   The (rational) factorization of x.  ;   <  t%                                                                     ؕ  ̔  ̕  |?  u%  
      	   __sig__14   @  @  v%         ̔  ԕ  X            B  w%           Returns the first n primes. XE  pE  x%                                                                       ̔  ܕ  XK  y%  
      	   __sig__15   L  L  z%            ̔                N  {%           Returns the first n primes. hP  P  |%                                                                       ̔    xT  }%  
      	   __sig__16   U  U  ~%            ̔                X  %  
         InitialPrimes   xY  %                                               %           Returns the first n primes. ]  ^  %                                                                       ̔    \b  %  
      	   __sig__17   4d  Ld  %            ̔                tf  %  
      
   PrimesUpTo  ph  h  %                                               %           Returns the nth prime.  m  %  
      	   __sig__18   lo  o  %  
      	   __sig__19   q  q  b  
         InertiaElement    c                 |q                              d  *         The known part of the local element x. Note that this function will be removed in the next release; Expand() should be used in its place.       e                                                                 |r  q  \q  q  <!  f  
         __sig__2 "  4"  \"  g            \q  q              #  h  @         The defining polynomial of a generator of L. It is an error if the degree of L is 1. If L is ramified it will be the polynomial defining the ramified extension; otherwise it will be the minimal polynomial of the inertial element -  -  i                                                                     q  \q  q  1  j  
         __sig__3 2  2  2  k            \q  q              4  l  2         The relative degree of L over a substructure. It is an error if the degree of L is 1. If L is ramified it will be the ramification degree, otherwise the degree of inertia  ;   <  m                                                                     q  \q  q  |?  n  
         __sig__4 @  @  @  o            \q  q              B  p        &   The degree f unramified extension of L  F  q                                                               q  q  \q  q  K  r  
         __sig__5 L  L   M  s            \q  q              O  t  
      	   LocalRing   8P  PP  u                 q                              v        >   The degree f unramified extension of L, reduced to precision n  U  w                                                             q  q  \q  q  4Z  x  
         __sig__6 [  P[  [  y            \q  q              ]  z        J   The totally ramified extension of L defined by the Eisenstein polynomial g  a  a  {                                                               q  q  \q  q  tf  |  
         __sig__7 h  ph  h  }            \q  q              Tj  ~  "      b   The totally ramified extension of L defined by the Eisenstein polynomial g, reduced to precision n  p  p  p  tq    
      
   LocalField                       r                                      >   The degree f unramified extension of L, reduced to precision n  
                                                               r  r  \q  r      
      	   __sig__18                   \q  r                        J   The totally ramified extension of L defined by the Eisenstein polynomial g  ,  t                                                                 r  r  \q  r      
      	   __sig__19                   \q  r              h            b   The totally ramified extension of L defined by the Eisenstein polynomial g, reduced to precision n  #  $                                                               r  r  \q  r  |'    
      	   __sig__20   <)  T)              \q  r               ,          3   The unramified local ring with prime p and degree f d/  |/                                                                 r  r  \q  r  2    
      	   __sig__21   3  84              \q  r              x5          @   The unramified local ring with prime p, degree f and precision n 9  9  4:                                                               r  r  \q  r  <    
      	   __sig__22   =  =              \q  r              ,@          S   The totally ramified local ring with prime p defined by the Eisenstein polynomial g D  D                                                                 s  r  \q  r  I    
      	   __sig__23   4L  LL              \q  r              M           c   The totally ramified local ring with prime p and precision n defined by the Eisenstein polynomial g Q  Q                                                               s  s  \q   s  XV    
      	   __sig__24   X  4X              \q  s              0Z          W   The local ring with prime p and inertia degree f defined by the Eisenstein polynomial g ^  ^  _                                                               $s  s  \q  s  8c    
      	   __sig__25   d  e              \q  s              g           d   The local ring with prime p, inertia degree f and precision n defined by the Eisenstein polynomial g l  l    
      	   __sig__26   o  Po              \q  (s              q  L                  u                              M        3   Return the level of the space M of modular symbols. T	  l	  N                         t                                        <  @u  8s  4u  p  O  
      	   __sig__12   H  `  P            8s  <u                Q        8   Return the base field of the space M of modular symbols.   H  t  R                         t                                           Pu  8s  Du  <  S  
      	   __sig__13   ,  D  T            8s  Lu              H  U        A   Return the Dirichlet character of the space M of modular symbols.   P!  x!  V                         t                                            `u  8s  Tu  X$  W  
      	   __sig__14   %  %  X        4 8s  \u  X            '  Y  
      	   Character   )  $)  Z                 Xu                                         Tn emona -  [        S   Return true iff working in the plus one quotient of the space M of modular symbols. 1  1  \                         t                                            xu  8s  lu  5  ]  
      	   __sig__15   6  6  ^        4 8s  tu  X            9  _  
         IsPlusQuotient  :  `                 pu                              a        S   Return true iff working in the plus one quotient of the space M of modular symbols. @  ,@  b                         t                                            u  8s  u  D  c  
      	   __sig__16   F  F  d        4 8s  u  X            H  e  
         IsMinusQuotient TK  f                 u                              g           Returns the sign of M.  O  h                         t                                            u  8s  u  R  i  
      	   __sig__17   T  T  j        4 8s  u  X            XV  k           Returns the isogeny class of A. X  X  X  l                         t                                            u  8s  u  \]  m  
      	   __sig__18   ^  _  n        4 8s  u  X            `  o  
         IsogenyClass a  Xb  p                 u                              q        W   Return Heilbronn matrices of determinant n, as given by Merel. Here n can be composite. Pj  hj  j  r                                                                     u  8s  u  o  s        	   __sig__19   r  dt  |t  t  )  
         ModularSymbols     *                 t                              +        [   Returns the space of modular symbols of weight k for Gamma_0(N), over the rational numbers.     ,                                                        t       t  t  8s  t    -  
         __sig__4       .            8s  t              t  /  R      '  Returns the space of modular symbols of weight k for Gamma_0(N), over the rational numbers. If sign=+1 then returns the +1 quotient, if sign=-1 returns the -1 quotient, and if sign=0 returns the full space. If sign is a positive prime, then the full space of modular symbols mod sign isreturned. X"  "  "  0                                                      t       t  t  8s  t  %  1  
         __sig__5 &  &  &  2            8s  t              $)  3        ^   Returns the the space of modular symbols of weight k for Gamma_0(N), over the finite field Fp.  /  4                                                    t       t  t  8s  t  <2  5  
         __sig__6 3  P3  h3  6            8s  t              5  7  "      n   Returns the space of modular symbols of weight k for Gamma_1(N) with character eps, over the rational numbers.  :  8                                                          t       t  t  8s  t  t=  9  
         __sig__7 >  ?  $?  :            8s  t              @  ;  "      n   Returns the space of modular symbols of weight k for Gamma_1(N) with character eps, over the rational numbers.  ,G  <                                                        t        u  t  8s  t  |L  =  
         __sig__8 M  M  M  >            8s  t              O  ?  T      4  Returns the space of modular symbols of character eps and weight k. The level and base field are specified by the DirichletCharacter eps. The third argument "sign" allows for working in certain quotients. The possible values are -1, 0, or +1, which correspond to the -1 quotient, full space, and +1 quotient. \  \  @                                                      t           u  8s  t  `  A  
         __sig__9 a  a  Xb  B        4 8s  u  X            d  C        4   Return the weight of the space M of modular symbols. h  h  D                         t                                            u  8s  u  l  E  
      	   __sig__10   o  Po  F        4 8s  u  X            q  r  dt  ^#                         8                                              8s  t    `#            8s  |              (  a#  "      n   Returns false if p does NOT divide the discriminant of the subalgeba of Hecke generated by T2, T3, T5, and T7.    b#                                                                       8s      d#            8s                  e#  
         TestDisc        f#                                               #           Artin eNM   g#        /   Returns the nth Atkin polynomial modulo p > 2n. $     (  h#                                                                     8s    \  i#  
      
   __sig__320     p  j#            8s                  k#  
         AtkinPolynomial   l#                                               u#  
      
   __sig__322 mial \*  m#  "      k   Returns the pth supersingular polynomial. The roots are the supersingular j-invariants in characteristic p.    p1  n#                                                                     8s     8  o#  
      
   __sig__321     48  p#            8s                L8  q#           SupersingularPolynomial C  r#                                               s#  ,         Returns a list of the supersingular j-invariants in characteristic p. However, it is *much* faster to use the command SupersingularBasis(Mestre(p)).    N  t#                                                                     ؍  8s  ̍  PT  v#            8s  ԍ              W  w#  6         Given a new factor A=A_f and a prime ell, returns Norm((ell+1-a_ell(f))*(ell+1+a_ell(f))). This is an integer divisible by the congruence primes relating A to a form at level N(A)*ell. f     f  x#                             t                                        8s  ܍  k  y#  
      
   __sig__323     l  z#            8s                ,m  {#  
      
   RibetRaise     @m  |#                                               }#                                                                     8s      s  ~#  
      
   __sig__324     s  #            8s                s  #  
      
   SerreModPQ     s  #                                               #                                                                 8s      t  #  
      
   __sig__325     0t  #            8s                Ht  #  
         SerreModPQTable   {           HeilbronnCremona        |                 u                              }        M   If n is prime, return Cremona's Heilbronn matrices; otherwise return Merel's.     ~                                                                      v  8s  u  0    
      	   __sig__21   (  @          4 8s  u  X                
      	   Heilbronn   <  T                   u                                      	   __sig__24 GenListToM uot                            w    t                         u           v  8s          
      	   __sig__22   !  8!              8s  v              "  !%                 d                              #%  8         Returns the sequence of data consisting of a generator of a Hecke eigenvector, the eigenvector norm, and the eigenvalues of the first t Hecke operators. The content of the cusp space follows. __sig__7 -  $%                                    /  &%           HeckeEigenvalues 1  1  1  '%                 p                              (%        %   The Cremona database reference for E.   x5  )%                         |                                                d:  *%  
         __sig__8 ;  <;  T;  +%                            <                 >              =  ,%           CremonaReferences   @  ,@  -%                 >                              .%        H   The Cremona database reference for linear Hecke eigenspace V of level N. G  DG  \G  /%                             t                                    Ĕ      L  0%  
      	   __sig__10   M  M  1%                            P  (          s/magma/       lar_2%        .   /home/was/magma/Kohel/elementary_arithmetic.mg 3%     4   .   /home/was/magma/Kohel/elementary_arithmetic.mg 4%        6   The representative of x mod n in the range (-n/2,n/2].  Z  5%                                                                   ܔ  ̔  Д  d_  6%  
         __sig__0 `  `  `  7%            ̔  ؔ              b  8%  
         BalancedMod d  d  9%                 Ԕ                              P%  
         __sig__6 heorem i  :%        .   Returns the Chinese remainder lift of a and b.  tl  ;%                         L    L                           L           ̔    dt  b%           Choose  u  t            8s  u                u  
         HeilbronnMerel    v                 u                              w        F   Return the Heilbronn matrices of determinant p, as defined by Cremona.    x                                                                     u  8s  u    y  
      	   __sig__20   (    z        4 8s  u  X              $                            $  $            H                T  $                                               $           /home/was/magma/Kohel/decomp.m ($           /home/was/magma/Kohel/decomp.m ($        K   Returns the sequence of vector subspaces stabilized by the Hecke operators. L  x   %                                                                         @  %  
         __sig__0   0  H  %                            L  %           HeckeDecomposition  t    %                                                %        P   Returns the sequence of vector subspaces of V stabilized by the Hecke operators. $  $%  L%  %                         t                                                 ()  %  
         __sig__1 *  D+  +  %                            `-  %  
         __sig__5 sition  /  
%                                                                     0        p2  	%  
         __sig__3          %              $              @  %                                                                     ,    \  8:  %           HeckeLinearDecomposition ;  p;  ;  %                 L                              %  (         The sequence of one dimensional vector subspaces stabilized by the Hecke operators, priority given to the divisors of the level N.  HD  `D  %                             t                                P  H    <  H  %  
         __sig__3 J  J  XK  %              D               M  %        '   The sequence of linear Hecke subspaces. O  O  O  %                         t                                      <  X    L  (S  %  
         __sig__4 T  T  T  %              T              V  %         `   Returns the sequence of generators for the linear Hecke-invariant subspaces of the Hecke module. ˸   __si%  
         __sig__4          %           HeckeThetaDecomposition `  %                 (                              %        8   Returns the eigenvalues of Hecke for the first n primes. nvariant su%                              u                                    x    t      %              |              %%  
         __sig__6        ,p   %           HeckeEigenvectors   0u  hu  &           Units sors              InitialManinSymbolGenListToSquot     0                   v                                                       t                               u           (v  8s      !    
      	   __sig__23   "  "          4 8s  $v  X            $             InitialManinSymbolGenListToM %  (&                    v                                                           t                                      <v  8s      `-              8s  8v              /                   v                                      Q   Returns a bound b such that T1, ..., Tb generate the Hecke algebra as a Z-module.   `
  
                           t                                        v  v  8s  v  0              8s  v              h    
      
   HeckeBound  `                     v                                      Q   Returns a bound b such that T1, ..., Tb generate the Hecke algebra as a Z-module.                                                                          v  8s  v      
      	   __sig__31                     8s  v              "          H   Return vector space with basis the lattice defined by the elements of B. $   %  H%                                                            t           v  8s  v  $)    
      	   __sig__32   @+  +              8s  v              \-             VectorSpaceZBasis   d/  |/                   v                                $      s   This function computes the Hecke module generated by a vector v. The result is returned as a subspace with Z-basis.  6  h6                           u    t                           t       w  v  8s  v  :    
      	   __sig__33   ;  ;              8s  v              <    
      	   HeckeSpan   $>  >                   v                                $      u   This function computes the Hecke module generated by a basis of V. The result is returned as a subspace with Z-basis.   \G                           t    t                           t           w  8s   w  L    
      	   __sig__34   M  M              8s  w              P             Compute data needed by FastTn.  Q                               t                                  (w  w  8s  w  U    
      	   __sig__35   W  W          4 8s  w  X   P         tY    
      
   FastTnData  Z  Z                   w                                                       t    t                                      0w  8s      a    
      	   __sig__36   c  c          4 8s  ,w  X   X         e                                   t                            Lw  <w  8s      Pj    
      	   __sig__37   k  Dl          4 8s  8w  X   \         n                   4w                                
      	   __sig__38   u  v                   4v                                         FastTn is                                t                                  `v  Pv  8s      6    
      	   __sig__25   8  $9              8s  Lv              :    
         HeckeOperator   ;                   Hv                                      E   Compute the n-th Hecke operator Tn on the space M of modular symbols.   @                               t                                      hv  8s  \v  lE    
      	   __sig__26   DG  \G              8s  dv              I                                   t                            v  tv  8s      N    
      	   __sig__27   O  P          4 8s  pv  X             TQ    
         TnSparse R  R  R                   lv                                "      g   Compute the action of the Hecke operator defined by the Heilbronn matrices Heil on the sparse vector v. Z  Z  Z                                   t                                v  8s  v  d_    
      	   __sig__28   `  `          4 8s  v  X   (         b    
      	   __sig__30 on d  d          )   Return sparse representation of vector v.   h  Th                           u                                            v  8s  v  tl    
      	   __sig__29   n  n          4 8s  v  X   ,         pq             SparseRepresentation u  u    ,         Compute the characteristic polynomial of the p-th Hecke operator Tn on the space M of modular symbols. Uses the modular algorithm, without proof.   `
  
    
      	   __sig__46   x                8s  w                                 w                                ,          Suppose A is a linear transformation of V which leaves the lattice L invariant. Returns A restricted to W, with respect to the basis Basis(W).                                                                      x  w  8s  w      
      	   __sig__47                   8s  w                 $                                                                          #  $  
         NewtonSlopes %  H%  $                                               $        	   __sig__15 ctorIndexes   T)  $  8         Make a list of forms in S_k(N,eps), with eps^2=1, and the correspoding index in the maximal order. The format of the list is [[degrees of eps], isogeny class, disc(O_f), index in max. order]. <2  T2  l2  $                                                                  8    ,  5  $  
      	   __sig__14   7  t8  $              4              4:  $           QuadraticModularFactorIndexes   ;  $                 0                              $                                                              L        $A  $              H              xC  $           SlopesOfUpGamma0 E  TE  lE  $                 D                              $                                                                 `        |M  $  
      	   __sig__16   $O  dO  $              \              P  $  
         factorpadic Q  Q  $                 X                              $        J   Return the p-adic slope alpha part of the polynomial f, to precision prec.  X  X  $                                                                x    l  ]  $  
      	   __sig__17   `^  ^  $              t              `  $  
         SlopeAlphaPart  a  $                 p                              $  
      	   __sig__19 a0 f  4g  $  ,         Returns the slope alpha part of the characteristic polynomial of T_p acting on S_k(Gamma_0(N)), with p-adic computations done to precision prec. n  o  Po  $                                                                    ,v  $  
      	   __sig__18   @w  w          ?   Compute action of Transpose(Tn) on the Hecke-stable subspace V. P                                           t                      Xw  Tw  8s  Hw  `          4 8s  Pw  X   `                                    t                                    hw  `w  8s      @    
      	   __sig__39                   8s  \w              T          ?   Compute action of Transpose(Tn) on the Hecke-stable subspace V.                                    t    t                             xw  pw  8s  dw      
      	   __sig__40                 4 8s  lw  X   h         "          ?   Compute action of Transpose(Tn) on the Hecke-stable subspace V. $  $  $                                   t    t                       w  w  8s  tw  (    
      	   __sig__41   *  *              8s  |w              ,          L   Compute action of Transpose(Tn), n in plist, on the Hecke-stable subspace V. 0  1                                   t    t                       w  w  8s  w  h4    
      	   __sig__42   `5  x5              8s  w              t8          L   Compute action of Transpose(Tn), n in nlist, on the Hecke-stable subspace V. ;  ;                               t    t                                 w  8s  w  >    
      	   __sig__43   D@  t@              8s  w              B    @         Compute the action of the Atkin-Lehner involution Wq on M, when this makes sense (i.e., trivial character, even weight). The Atkin-Lehner map Wq is rescaled so that it is an involution, except when k>2 and char(F) divides q. M  M  M                               t                                  }  w  8s  w  Q    
      	   __sig__44   R  $S              8s  w              0U             Wq  (V  XV                   w                              4           Sk bols  Z    ,         Compute the conjugation involution * on V. This involution is defined by the 2x2 matrix [-1,0,0,1]; it sends X^i*Y^j{u,v} to (-1)^j*X^i*Y^j {-u,-v}. a  pa                           t                                            w  8s  w  @f    
      	   __sig__45   h  Th              8s  w               j    
         StarInvolution  k                   w                                                       t                                          w  8s  w  ,v             Tnpoly   w  "        D   Compute the action of T_p on a subspace of integral modular symbols.   P  #                             t                                      x  8s  x  (  b$           CoefficientValuation   p  c$                 |                              l$           __sig__8 ionPrimeToP   @  d$         d   Returns the valuation of the ideal generated by the coefficients a_n of f with n not divisible by p.   t  e$                             #                                             g$                            h  h$           CoefficientValuationPrimeToP       i$                                               j$        /   Cast g, which should be in Z[[q]], to lie in R. $   %  H%  k$                         #   $                          #                $)  m$                            +  n$  
         CastPowerSeries \-  o$                                               p$        K   Truncate f so that q^prec is the highest possible power of q involved in f. 3  43  q$                             #                          #          ̑       7  r$  
         __sig__9 9  <9  9  s$              ȑ              :  t$           TruncatePowerSeries ;  ;  u$                 đ                              v$  "      j   Returns a sequence of tuples <[N,iso,dim],[cp1,cp2,...],[wp1,wp2,...]>, one for each new factor of J_0(N).  @C  xC  w$                                                                       ؑ  G  x$  
      	   __sig__10   0J  TJ  y$                            L  z$  
         ComponentGroups M  {$                 ܑ                              |$         c   Returns a sequence of triples <dim,[cp1,cp2,...],[wp1,wp2,...]>, one for each new factor of J_0(N). U  0U  }$                                                                       tY  ~$  
      	   __sig__11   Z  Z  $                            ]  $  
      	   __sig__13 nt ^  ^  $                                                                           b  $  
      	   __sig__12   d  d  $                            4g  $           ComponentGroupsPrint i  Hi  $                                                $  *         Returns the sequences of slopes of the Newton polygon of f with at the prime p. The slopes are the valuations of the p-adic roots of f. v  v  ,v  $                            w  w  Dx    
         Restrict                          w                                ,          Suppose A is a linear transformation of V which leaves the subspace W invariant. Returns A restricted to W, with respect to the basis Basis(W).    H  `                           t                                      x  x  8s  x      
      	   __sig__48                   8s  x                        ]    Suppose A leaves W invariant. Returns A restricted to W, with respect to the basis Basis(W).                              8                                      (x   x  8s  x  8!    
      	   __sig__49   0"  X"              8s  x              #  	  2          Suppose A is a linear transformation of V which leaves the subspace W spanned by the vectors listed in B invariant. Returns A restricted to W, with respect to the basis B. +  +  
                                                                   0x  8s  $x  /    
      	   __sig__50   41  L1              8s  ,x              2    >         Suppose B is a basis for an n-dimensional subspace of some ambient space and A is an nxn matrix. Then A defines a linear transformation of the space spanned by B. This function returns the kernel of that transformation. ;  ;                                                          t       Lx  @x  8s  4x  $?    
      	   __sig__51   @  @          4 8s  <x  X            B    
         KernelOn D  D  D                   8x                                                       t                               t           Tx  8s      L    
      	   __sig__52   M  M          4 8s  Px  X            P          ^   Compute the action of the Hecke operator Tn with respect to the basis for the subspace V of M.  tT                               t    t                                dx  8s  Xx  hX    
      	   __sig__53   Z  0Z              8s  `x              [    
         HeckeOperatorOn ]                   \x                                      9   Compute the action of Tn on the integral modular symbols.   c  d                               t                                      |x  8s  px  i    
      	   __sig__54   8j  Pj              8s  xx              tl              HeckeOperatorMkZ n  o  Po  !                 tx                              $  
      	   __sig__55   v  ,v  %            8s  x              w  9$                 Ԑ                              :$        P   Given a space M of modular symbols and a field F, attempt to compute M tensor F. 
  `
  
  ;$                              t                           t             8s    0  =$        4 8s    X   `         h  >$           /home/was/magma/Hecke/apps.m 0:?$     ,      /home/was/magma/Hecke/apps.m 1:@$                         #                                                   A$  
         __sig__0       B$                              C$  
      	   OrderList       D$                                                E$        Z   Twists the q-expansion f by the Dirichlet character eps, thus returning sum eps(n)*a_n(f).  %  %  F$                              #                          #                 )  G$  
         __sig__1 +   ,   ,  H$                            -  J$                                               $           fcp able es K$  0         Compute the Zp-rational newforms associated to f. The precision of Zp is of course not infinite; it is actually O(p^20), which could cause problems. Be careful! 8  8  $9  L$                                                                 D  8    ,  ;  M$  
         __sig__2 <  <  <  N$              4              >  O$           ZpRationalNewforms  @  @  P$                 0                              Q$                                                     t       T  L        G  R$  
         __sig__3 I  0J  TJ  S$              H              L  T$        4   Returns a list of the the Zp-rational newforms in M. O  O  U$                                 t                                \    P  $S  V$  
         __sig__4 T  T  T  W$              X              V  X$        ?   Returns the power series sum_{n not divisible by p} a_n(f) q^n. `Z  tZ  Z  Y$                             #                          #          l    `  _  Z$  
         __sig__5 `  t`  `  [$              h              Xb  \$  
         pDeprive d  0d  Hd  ]$                 d                              f$  
         __sig__7 ion i  Hi  ^$        F   Returns the valuation of the ideal generated by the coefficients of f.  m  _$                         #                                               x  du  `$  
         __sig__6 v  @v  Tv  a$                            Dx  &           HeckeOperatorSkZ   H  `  '                 x                              (  .         Given a cusp a=[u,v] this function finds the index i and a scalar alpha such that a = alpha*(i-th standard cusp). It then returns the tupple <alpha, i>.       )                             t                                      x  8s  x    *  
      	   __sig__56   <  T  +        4 8s  x  X              ,  
      
   CuspToFree  l    -                 x                              .           Compute the Boundary map.       /                         t                                 w           x  8s  x  "  0  
      	   __sig__57   #  #  1        4 8s  x  X            %  3                         t                                 t           x  8s         2  
      	   __sig__60           5            8s  x              -  <                 x                              6  
         CuspidalSymbols <2  7                 x                              8        <   Return the subspace of S_k(N,Q) of cuspidal modular symbols. 7  t8  9                         t                                 t           x  8s  x  ;  :  
      	   __sig__59   t<  <  ;        4 8s  x  X            =  C  
      	   __sig__62 mbols ?  =                         t                                 t           x  8s      D  >  
      	   __sig__61   E  F  ?            8s  x              G  Q                                                                   Ly  8s        $                                                                     <  8s  0  d  $            8s  8                $           Volume  d  $                 4                              $        B   Compute the norm of an element of a quotient of a polynomial ring.  @  X  $                         o                                           T  8s  H  0  $  
      
   __sig__354       $            8s  P              l  $           Returns the word for nth.         $                                                                     d  8s  X  #  $  
      
   __sig__355  $%  L%  $            8s  `              &  $           ToNth   '  $                 \                              $        #   The sequence of primes [p1 ... p2]. -  -  $                                                                   |  8s  p  1  $  
      
   __sig__356  2  2  $            8s  x              4   $  
         PrimeSeq 5  5  5  !$                 t                              I$           Twist   ter "$        -   Base extend the character eps to the field F.   0<  #$                                                                      8s    ?  $$  
      
   __sig__357  A  (A  %$        4 8s    X   P         |C  &$           BaseExtendCharacter XE  pE  '$                                               ($        &    Base extend the mlist to the field F.  PL  )$                                                                      8s     P  *$  
      
   __sig__358  Q  (Q  +$        4 8s    X   T         R  ,$  
         BaseExtendMlist T  -$                                               .$        %    Base extend the quot to the field F.   Y  /$                                                                    Đ  8s    ]  0$  
      
   __sig__359  _  _  1$        4 8s    X   X         ta  2$  
         BaseExtendQuot  <c  3$                                               <$  
      
   __sig__361 tion Xh  4$        /   Base extend the decomposition D to the field F. 0k  Tk  lk  5$                                                                    ܐ  8s  А  p  6$  
      
   __sig__360  0u  hu  7$            8s  ؐ              v  8$           BaseExtendDecomposition x  %              @           IntegralCuspidalSymbols PL  A                 x                              B                         t                                 t           y  8s      Q  D            8s  y              T  E           SkZ U  4U  F                 y                              G                         t                                 t           $y  8s      [  H  
      	   __sig__63   x]  ]  I            8s   y              _  T           DegeneracyCosetReps      U                 Dy                              V        E   If possible compute the map M1 --> M2 corresponding to the integer d.   `  W                         t    t                                  ty  dy  8s  Xy    X  
      	   __sig__66       Y            8s  `y                Z  
         DegeneracyMap   $  [                 \y                              \  Z      I  If possible compute the degeneracy map M1 --> M2 corresponding to the integer d. Here M1 and M2 are spaces of modular symbols, of the same weight and d is a divisor of the quotient of the two levels N1 and N2. If the N1 divides N2 then the "raising" map is computed, if N1 is divisible by N2, then the "lowering" map is computed.   %  $&  ]                             t    t                                |y  8s  py  *  ^  
      	   __sig__67   8,  X,  _        4 8s  xy  X            .  `        V   Returns the space Mk(NN,eps') associated to Mk(N,eps). Here NN must be a divisor of N.  <2  a                             t                           t           y  8s  y  x5  b  
      	   __sig__68   7  `7  c        4 8s  y  X            9  d           OldModularSymbols   ;  $;  e                 y                              f            Returns the p-new subspace of M. >  ?  $?  g                             t                           t           y  8s  y  xC  h  
      	   __sig__69   E  <E  i        4 8s  y  X            \G  j  
         pNewSubspace H  I  k                 y                              l        %   Returns the p-new subspace of M dual.   dO  m                             t                           t           y  8s  y  @R  n  
      	   __sig__70    T  tT  o        4 8s  y  X            V  p           pNewDualSubspace X  X  4X  q                 y                              r                         t                                 t           y  8s      _  s  
      	   __sig__71   t`  `  t        4 8s  y  X             Xb  v                 y                                         MkZ nSymbol w                         t                                 t           y  8s      hk  x  
      	   __sig__72   l  m  y        4 8s  y  X   $         o  z           CuspidalNewSubspace |t  t  {                 y                              |            Returns the p-new subspace of M. x   y  y  (y  <y  J           SkZPlus pa  K                 y                              L                         t                                 t           8y  8s      Hi  M  
      	   __sig__64   hj  j  N            8s  4y              l  O  
         SkZMinus n  o  Po  P                 0y                              u           Sknew ce  s R  
      	   __sig__65   v   w  S        4 8s  Hy  X             x   y  y    
      	   Mknewdual                        z                                                       t                                 t           $z  8s      `    
      	   __sig__75   X  p          4 8s   z  X   0             
      	   Sknewdual                        z                                
      	   __sig__77 space $                           t                                 t           8z  8s          
      	   __sig__76               4 8s  4z  X   4           #        @   Create a table of odd parts of BSD data for N between N1 and N2. !  !  !  #                                                           8    8s    $  #           TableCongruenceR &  l&  &  #                                               #        >   Append the level N of the congruence table to the file "name".  \-  #                                                                 Џ  8s  ď  L1  #  
      
   __sig__347  T2  l2  #            8s  ̏              84  #                                                             ܏  8s      8  #  
      
   __sig__348  9  4:  #            8s  ؏              T;  #  
         TableConnected  \<  #                 ԏ                              #  *         Create a table of connectedness of abelian intersection graph in the "box" T_k(Gamma_0(N)), where N1 <= N <= N2 (N prime) and k1 <= k <= k2. E  lE  #                                                             8s    TK  #  
      
   __sig__349  L  L  #            8s                N  #                                                                        8s      Q  #  
      
   __sig__350  S  S   $            8s                U  $           Returns the odd part of n.  W  X  $                                                                       8s    [  $  
      
   __sig__351  t]  ]  $        4 8s    X   8         _  $                                               $                                                                    $  8s      4g  $  
      
   __sig__352  h  i  	$            8s                 j  
$           DotProd Dl  $                                               $  *         Compute the absolute value of the determinant of the matrix got by finding a Z-lattice basis for the Z-span of the rows in the sequence L.  x  x  $  
      
   __sig__353  y  y  }                         t                                 t           y  8s  y  	  ~  
      	   __sig__73   	  8
          4 8s  y  X   (             
         NewSubspace                      y                                                       t                                 t           z  8s      t    
      	   __sig__74     t          4 8s  z  X   ,         \  #  (         Create a table of factored characteristic polynomials of Tp on S_k(Gamma_0(N)) for N between N1 and N2 and p between p1 and p2. 	  	  	  #                                                           8s      #            8s                  #  
         TableCharpoly     #                                               #        '   Create a table of congruence numbers r. for N betwee#                                                           ȏ  $  8s       #  
      
   __sig__346     j#            8s  (              8s  #  
         TableBSD "  4"  \"  #                                               #        7   Append the level N of the BSD table to the file "name". &  &  &  #                                                                 @  8s  4  $,  #  
      
   __sig__339  -  -  #            8s  <              /  #        @   Create a table of odd parts of BSD data for N between N1 and N2. 2  2  2  #                                                           `  P  8s  D  l6  #  
      
   __sig__340  8  8  #            8s  L              h:  #  
         TableBSDFull ;  X;  #                 H                              #        7   Append the level N of the BSD table to the file "name". 0@  H@  x@  #                                                                 h  8s  \  D  #  
      
   __sig__341  F   G  #            8s  d              H  #        B   Create a table of rational parts of special values of L-functions.  hM  M  #                                                             x  8s  l  (Q  #  
      
   __sig__342  R  DR  #            8s  t              T  #  
         TableLRatio U  V  #                 p                              #  
      
   __sig__345 s Z  dZ  #        '   Create a table of splittings of J_0(p).  ]  H]  `]  #                                                               8s    ta  #  
      
   __sig__343  c  <c  #            8s                Pe  #           TablePrimeSplittings g  g  #                                               #        0   Append the level p of the prime splitting table. m  Dn  \n  #                                                                   8s    u  #  
      
   __sig__344  v  v  #            8s                x  #            8s                y             CuspidalNewDualSubspace                    0z                                      #   Returns the new subspace of M dual. !  !                           t                                 t           Pz  8s  Dz  $          4 8s  Lz  X   8         &    
         NewDualSubspace '                   Hz                                8         Computes the image in M2 of x in M1 under the theta operator q*d/dq : M1 --> M2. Thus M1 and M2 should be spaces of modular symbols mod ell of the same level, and Weight(M2) = Weight(M1)+ell+1.   T3  l3                           u    t    t                     u           hz  8s  \z  d7    
      	   __sig__78   9  9              8s  dz              :  #                                                                   |  8s        #            8s  x              	  #  
         ArtinOrderTwo   
  #                 t                              #           Given an integer N that is coprime to 5; a sequence [d1,...,dr] of degrees which define a mod N character eps; and a sequence [p1,p2,...,pn] of primes p such that a_p=0; this function computes the subspace ker(Tp1') meet ker(Tp2') ... meet ker(Tpn') of the space M_2(Gamma_1(5*N),eps_5*eps;F5bar)^+. (Primes denote transpose.) The first argument returned is the subspace W, and the second is the space of modular symbols. The subspace W is a subspace of the dual and can be computed efficiently using FastTp.   #  #                                                      t t             8s    &  #  
      
   __sig__331  (  (  #            8s                +  #                                               $           OddPart  /  #  "      h   Returns the modular symbols factor corresponding to the nth curve from the paper "Empirical evidence..." 3  3  3  #                                                          t           8s    t8  #  
      
   __sig__332  9  9  #            8s                $;  #  
         EvidenceCurve   ,<  #                                               #  4         Returns the modular symbols factor corresponding to the curve from the paper "Empirical evidence..." labeled s. Here s is given by the notation in that paper. E.g., "29", or "65,A".   ,G  #                                                          t           Ď  8s    |L  #  
      
   __sig__333  M  M  #            8s                O  #                                                          t           Ў  8s      $S  #  
      
   __sig__334  T  T  #            8s  ̎              V  #  
         EvidenceLabel   hX  #                 Ȏ                              #        7   Create a table of eigneforms on Gamma_0(N) of weight k. ^  `^  ^  #                                                           8s  ܎  b  #  
      
   __sig__335  d  d  #            8s                4g  #  
         TableEigenforms i  #                                               #        E   Append the level N data for the table of eigenforms to the file name.   (p  #                                                                8s    v  #  
      
   __sig__336  hx  x  #            8s                y  #  
      
   __sig__337  lz  z    
         ThetaOperator   \<                   `z                                      #   Returns the winding element {0,oo}. @  @                           t                                 u       z  z  8s  tz  lE    
      	   __sig__79   DG  \G              8s  |z              I    
         WindingElement  LL                   xz                                      &   Returns the winding submodule T{0,oo}.  P                           t                                 u       z  z  8s  z  T    
      	   __sig__80   U  V              8s  z              4X             WindingSubmodule Y  Z  0Z                   z                                      9   Returns the winding element X^(i-1)*Y^(k-2-(i-1))*{0,oo}.   D`  \`                               t                           u           z  8s  z  d    
      	   __sig__81   Xf  pf              8s  z              i          <   Returns the submodule Te spanned by the ith winding element. l  tl                               t                           t           z  8s  z  dt    
      	   __sig__82   u  v              8s  z              w                               t                                  z  z  8s      Tz    
      	   __sig__96               4 8s  {  X                
         ToIsogenyCode   	                   {                                
      
   __sig__100 isor           2   Returns the number n so that s = ToIsogenyCode(n).                                                                           {  8s  {  (    
      	   __sig__97   l                8s  {                "                                                                   ċ  8s      "            8s                  "  
         LinearRelations    "                                               "                                                                   ؋  8s      $&  "  
      
   __sig__299  &  '  "            8s  ԋ              T)  "           MonomialsOfDegreeD   ,   ,  "                 Ћ                              "                                                                  8s      <2  "  
      
   __sig__300  P3  h3  "            8s                5  "           RelationsOfDegreeD  6   7  "                                               "                                                                      8s      <  "  
      
   __sig__301  =  =   #            8s                ,@  #        O   Compute the dimension of the space of cusp forms of character eps and weight k. D  D  D  #                                                                    8s    I  #  
      
   __sig__302  4L  LL  #            8s                M  #  
         DimensionSk O  O  #                                               #        K   Compute the dimension of the space of cusp forms on Gamma_0(N) of weight k. XU  U  #                                                                   (  8s    Y  	#  
      
   __sig__303  [  ([  
#            8s  $              \]  #           Returns dim S_k(Gamma_1(N)). _  _  #                                                                   8  8s  ,  d  #  
      
   __sig__304  de  e  #            8s  4              Th  #  
         DimensionSkG1   i  #                 0                              #                                                                     L  8s      dt  #  
      
   __sig__305  u  v  #            8s  H              w  #  
         DimensionS2 x  x  #                 D                              1#           TpSS ularJ    &      x   Given a Manin symbol [P(X,Y),[u,v]], this function computes the corresponding element of the space M of Modular symbols. 	  	  8
    
      	   __sig__89   H  `          4 8s  @{  X   x             
      	   __sig__93 bol             -   Returns the modular symbol {alpha,beta} in M.                                      t                     u       d{  T{  8s  H{      
      	   __sig__90   <  \              8s  P{                           ConvFromModularSymbol                      L{                                H         Given a modular symbol P(X,Y)*{alp,beta}, FromModularSymbol returns the corresponding element of M. The input is a pair <P,x>, where P is a polynomial in X and Y, and x=[[a,b],[c,d]] is a pair of elements of P^1(Q), where [a,b] <--> a/b and [c,d] <--> c/d. )  )  )                               t                           u       t{  l{  8s  `{  /    
      	   __sig__91   40  l0          4 8s  h{  X            1    N        Given a sequence of modular symbols P(X,Y)*{alp,beta}, FromModularSymbol returns the corresponding element of M. The input is a sequence of pairs <P,x>, where P is a polynomial in X and Y, and x=[[a,b],[c,d]] is a pair of elements of P^1(Q), where [a,b] <--> a/b and [c,d] <--> c/d.  t<  <                               t                           u           |{  8s  p{  t@    
      	   __sig__92   A  A          4 8s  x{  X            D          R   Tests the modular symbols conversion routines. Must always return the basis for M.  H  I                          t                                           {  8s  {  M              8s  {              P    
         TestConv P  Q  $Q                   {                                
      	   __sig__95 bols  0U          =   Return the sub Z-module M_k(N,Z) of integral modular symbols.   X                           t                                 t           {  8s  {  ]    
      	   __sig__94   `^  ^              8s  {              `             IntegralModularSymbols  Xb                   {                                                       t                                 t           {  8s       j              8s  {              Dl             IsogenyCodeToInteger   $                   {                                                                                               |  {  8s          
      	   __sig__98               4 8s  {  X                          SmallestPrimeNondivisor                    {                                      K   Return the smallest prime number ell not dividing N and such that ell >= p. x                                                                       |  8s  |  |    
      	   __sig__99   t            4 8s  |  X            |!             Returns the nth prime.  "                                                                       $|  8s  |  (&  	        4 8s   |  X            '  
  
         NthPrime )  @)  X)                   |                                      1   Returns the integer n so that p is the nth prime.   /   0                                                                   L|  <|  8s  0|  83    
      
   __sig__101  4  4          4 8s  8|  X            l6    
         PrimePos 8  8  8                   4|                                      H   Returns the position of the divisor p of N, or 0 if p does not divide N. =  `=  x=                                                                     T|  8s  H|  A    
      
   __sig__102  DC  |C              8s  P|              pE             Fast, non-proved, charpoly. G  G                                                                       d|  8s  X|  0M    
      
   __sig__103  N  O          4 8s  `|  X            P    
         ModularCharpoly Q                   \|                                                                                                   x|  8s      lX    
      
   __sig__104  Z  4Z          4 8s  t|  X            [    
         FactorCharpoly  ]                    p|                              !        >   Compute integer kernel of the not-necessarily-square matrix A.  d  "                         w                                 8       |  |  8s  |  i  #  
      
   __sig__105  <j  Tj  $            8s  |              xl  %  
         IntegerKernel   n  &                 |                              '        >   Compute integer kernel of the not-necessarily-square matrix A.  w  (                         D                                 8       |  |  8s  |  Xz  )        
   __sig__106  {  {  {  {                   {                              Y           IsNew n ns          F   Returns the n-th isogeny coding. The coding goes A,B,C,...,Z,AA,BB,...  x                                                                       {  8s  {  {  "                                               "  H         Let eps_p denote the character obtained by restricting eps to the p-factor. This function returns eps_p(n). When gcd(p,n)>1 this is 0. When gcd(p,n)=1, let m be an element of (Z/NZ)^* which is 1 mod q for all q neq p and is n at p. Then eps_p(n) = eps(m).       "                                                                 8  8s  ,    "            8s  4                "                                                                   D  8s        "  
      
   __sig__292      "        4 8s  @  X   |            "        N   Returns true iff M>=1 divides Modulus(eps) and is divisible by Conductor(eps).  #  "                                                                   T  8s  H   '  "  
      
   __sig__293  )  ()  "        4 8s  P  X            +  "  
         CanReduceModM   `-  "                 L                              "  
      
   __sig__296 ers  P1  "  *         Given a Dirichlet character eps, such that M divides Level(eps) and Conductor(eps) divides M, return the associated mod M Dirichlet character.  7  "                                                                   l  8s  `  (;  "  
      
   __sig__294  <  0<  "        4 8s  h  X            x=  "           AssociatedModMCharacter |?  "                 d                              "        G   Returns a sequence consisting of all of the mod N Dirichlet characters. F  F   G  "                                                                       8s  x  PL  "  
      
   __sig__295  hM  M  "            8s                O  "           AllDirichletCharacters  P  "                 |                              "        
   __sig__297 erClasses U  4U  "         a   Returns a sequence consisting of the Gal(Qbar/Q)-conjugacy classes of mod N Dirichlet characters.   LZ  dZ  "                                                                       8s    ^  "            8s                `  "           AllDirichletCharacterClasses b  b  "                                               "         f   Print a Dirichlet character. This is a temporary function, while I wait for classes or "hack objects".  lk  "                                                                     8s    p  "            8s                u  "  .         Let P be a sequence of power series (or polynomials) over the integers. This function returns a basis for the Z-linear relations satisfied by these series. z  z  "  
      
   __sig__298  {  |  *            8s  |                +        '   Compute integer kernel of the matrix A. 	  (	  @	  ,                                                          8           |  8s  |  D  -  
      
   __sig__107    4  .            8s  |              l  /        E   Compute integer kernel of the matrix A, and return as integral space.   x  0                                                          8           |  8s  |  @  1  
      
   __sig__108  0  H  2            8s  |              L  3  
         IntegerKernelZ    4                 |                              5        U   Compute the linear combinations of the elements of B defined by the elements of Comb.   $  6                                                                   |  8s  |  (  7  
      
   __sig__109  *  *  8        4 8s  |  X            ,  "         Create a Dirichlet character modulo N. The input zeta is a root of unity in some field. The second input "degs" is a list of nonnegative integers. We explain the notation we use for degs. There is an isomorphism Z/NZ ---> (Z/p1^(i1)Z) x (Z/(p2)^(i2)Z) x ... with p1 < p2 < ... the primes dividing N. Passing to units we find that each factor in the right hand side is a cyclic group, except possibly when p1=2 in which case the cyclic group is trivial, or a group of order 2 times a cyclic group (possibly trivial). The degs specify the order that the image of a primitive root of each Z/p^iZ should map to. The primitive root used is the one computed using the function PrimitiveRoot(p^i). In the special case p=2 and i>=3, one should supply supply two entries corresponding to 2 in the degs sequence, because the group (Z/2^nZ)^* is generated by -1 and 5. The entries in the gens sequence correspond bijectively, and in order, to the prime divisors of N, listed in increasing order. Note: Not every character can be described in this way.    $/  L/  "                                                               Ȋ    8s    l2  "        4 8s    X   X         84  "        '   Create the trivial Dirichlet character. h6  6  6  "                                                                 ؊  Њ  8s  Ċ  :  "  
      
   __sig__285  ;  ;  "            8s  ̊              ,=  "        ]   Create the trivial Dirichlet character with values in the prime field of characteristic p>=0.   A  "                                                                     8s  Ԋ  F  "  
      
   __sig__286  G  H  "            8s  ܊              K  "        ^   Evaluate the character eps on the matrix gamma=[a,b, c,d] in Gamma_0(N). The result is eps(a).  P  "                                                                   8s    S  "  
      
   __sig__287  U  0U  "        4 8s    X   h         hW  "        ,   Evaluate the character eps at the integer n. Z  0Z  "                                                                    8s    ^  "  
      
   __sig__288  _  ,`  "        4 8s    X   l         a  "        4   Evaluate the character eps at the integer (n mod N). e  Le  "                         L                                            8s     j  "  
      
   __sig__289  k  k  "        4 8s    X   p         Xn  "        ,   Evaluate the character eps at the integer n. r  dt  "                         L                                    0     8s    Dx  "  
      
   __sig__290  (y  <y  "            8s                Tz  "  
         EvaluateAtp {  {  "        
   __sig__291  |  |  |  |  9           LinearCombinations  /  /  :                 |                              ;                         t                               t       }  |  8s      5  <  
      
   __sig__110  6  6  =            8s  |              9  >  
         IntegerKernelOn :  ?                 |                              @  F         Suppose B is a basis for an n-dimensional subspace of some ambient space and A is an nxn matrix. Then A defines a linear transformation of the space spanned by B. This function returns the integer kernel of that transformation, as a subspace with basis.   \G  A                                                        t           }  8s   }  L  B  
      
   __sig__111  M  M  C            8s  }              P  D            Compute the lattice index [V:W]. Q  Q  Q  E                                                                   }  8s  }  V  F  
      
   __sig__112  W  X  G            8s  }              Y  H  
         LatticeIndex [  ([  I                 }                              J  "      g   Returns true if and only if A is a root in the ModSymParent tree, i.e., if and only if A has no parent. 8c  c  c  K                         t                                            4}  8s  (}  h  L  
      
   __sig__113  i   j  M        4 8s  0}  X             Dl  N  
         ModSymIsRoot n  Xn  O                 ,}                              P        3   Returns the parent of the modular symbols factor A. v  v  Q                         t                                 t           L}  8s  @}   z  R  
      
   __sig__114  z  {  S        4 8s  H}  X   $         ||  |  |  ^  
      	   OldFactor       _                 l}                              `        (   List the dimensions of the factors in D. 
  `
  
  a                                                                     }  8s  }  0  b  
      
   __sig__117    0  c            8s  }                d           List the Shas of factors in D.  t  e                                                                 ؄  }  8s  }  <  f  
      
   __sig__118  ,  D  g            8s  }              H  h           Sha     i                 }                              ~           J0 forms "  j        6   Returns the number of newforms in the decomposition D.  $  k                                                                     }  8s  }  t(  l  
      
   __sig__119  )  *  m            8s  }              ,  "  (         Using the standard vector std, this function creates a Dirichlet character modulo N that takes values in a field of characteristic p.   l2  "                                                                 8s  |  5  "            8s                8  "           DirichletCharacter  L:  d:  "                                               "       (  Create any Dirichlet character modulo N in characteristic p. The input "pows" is a list of nonnegative integers. There is an isomorphism Z/NZ ---> (Z/p1^(i1)Z) x (Z/(p2)^(i2)Z) x ... with p1 < p2 < ... the primes dividing N. Passing to units we find that the right hand side is a cyclic groups, except possibly when p1=2 in which case the cyclic group is trivial, or a group of order 2 times a cyclic group (possibly trivial). Let zeta be a primitive rth root of unity in the algebraic closure of the prime field of characteristic p. The pows specify the power of zeta that a primitive root (computed using PrimitiveRoot(p^i)) of each Z/p^iZ maps to. The primitive root used is the one computed using the function PrimitiveRoot(p^i). In the special case p1=2 and i1>=3, the user must supply two entries in the pows sequence. (But if i1=1 or 2, then the user must supply exactly one entry.) The group (Z/2^nZ)^* is generated by -1 and 5. The entries in the pows sequence correspond bijectively, and in order, to the prime divisors of N, listed in increasing order.  i  0i  Hi  "                                                               8s    m  "  
      
   __sig__282  o  o  "        4 8s    X   L         t  "                                                                 8s    x  "  
      
   __sig__283  Py  hy  "        4 8s    X   T         z  "           Create Dirichlet character. (|  @|  "  
      
   __sig__284  P}  d}  T  
         ModSymParent      U                 D}                              V                         t                                            `}  8s        W  
      
   __sig__115      X        4 8s  \}  X   (           Z                 X}                              [                         t                                 t           t}  8s        \  
      
   __sig__116  <  \  ]            8s  p}                        -   Returns the sum of all cuspidal factors of M.                               t                                 t           T~  8s  H~  
              8s  P~                F"  
      
   __sig__263      G"            8s                  H"  
         ClassicalPeriod   I"                                               J"        @   Returns the classical period r_j(f) = int_{0}^{ioo} f(z) z^j dz.   @  `  K"                                 t                     V           4  8s  (  L  L"  
      
   __sig__264      M"            8s  0              <!  N"        N   Compute the G_1 function defined in section 2.13 of Cremona's Algorithms book.  $  O"                         V                                 V           D  8s  8  '  P"  
      
   __sig__265  @)  X)  Q"            8s  @              $,  "                                                                       8s    p0  "        4 8s     X   0         1  "  
         CharacterLevel  2  "                                               "        0    Return true iff the Dirichlet character is odd. 8   9  (9  "                                                                       8s     <  "  
      
   __sig__276  <   =  "            8s                >  "        F    Returns the field in which the Dirichlet character eps takes values.   B  "                                                                     ,  8s     `G  "  
      
   __sig__277  H  I  "        4 8s  (  X   8         PL  "  
         FieldOfValues   M  "                 $                              "  
      
   __sig__279 mages Q  "                                                                     @  8s      4U  "  
      
   __sig__278  pV  V  "        4 8s  <  X   <         X  "           DirichletCharacterImages Z  Z  Z  "                 8                              "        -   Returns the standard vector that defines eps.   `  "                                                                     X  8s  L   e  "            8s  T              g  "  
         StandardVector  Li  "                 P                              "        ;   Returns the orders of the images of the factors (Z/p^iZ)^*. p  ,p  "                                                                     p  8s  d  v  "  
      
   __sig__280  lx  x  "            8s  l              y  "  
         ImageOrders pz  z  "                 h                              "        
   __sig__281  |}  }  }  }  n           NumberOfNewforms       o                 }                              x  
      
   __sig__121 tors "  p        >   Returns the number of cuspidal factors in the decomposition D.  $  q                                                                     }  8s  }  x(  r  
      
   __sig__120  )  *  s            8s  }              ,  t           NumberOfCuspidalFactors /  u                 }                              v        0   List the Atkin-Lehner signs of the factors in D. 3  T3  l3  w                                                                     }  8s  }  d7  y            8s  }              9  z        B   Compute J_0(N). (Really this is a decomposition of H1(X_0(N),Z)^+.  H<  `<  {                                                                     }  8s  }  0@  |  
      
   __sig__122  tA  A  }            8s  }              `D             FullCuspidalFactor                        L~                                      9   Compute the Hecke decomposition of the old subspace of M.     (                           t                                            l~  8s  `~      
      
   __sig__128                  8s  h~                           OldDecomposition     $                   d~                                      ;   Compute the Hecke decomposition of the *NEW* subspace of M.                              t                                        x  ~  8s  x~       
      
   __sig__129   "  "          4 8s  ~  X   t         x#          ;   Compute the Hecke decomposition of the *NEW* subspace of M. <&  T&                           t                                            ~  8s  ~  *    
      
   __sig__130  x,  ,          4 8s  ~  X   x         /             NewDecomposition 0  0  0                   ~                                      %   Compute the Hecke decomposition of M.   4                           t                                            ~  8s  ~  9    
      
   __sig__131  |:  :              8s  ~              ;             FullDecomposition   <  <                   ~                                                       t                                 t           ~  8s      \D    
      
   __sig__132  TE  lE              8s  ~              G                   ~                                                       t                                            ~  8s      O    
      
   __sig__133  P  P          4 8s  ~  X            Q    
      
   IsCuspidal  S  T                   ~                                         WqOn W  X                           t                                            ~  8s      [    
      
   __sig__134  t]  ]          4 8s  ~  X            _    
         IsEisenstein `  8a                   ~                                      :   Compute the action of the Atkin-Lehner involution Wq on A.  h  Th                               t                                         8s  ~  tl    
      
   __sig__135  n  n              8s  ~              pq                   ~                                      5   Returns the sign of the Atkin-Lehner involution on A.   x                           t                                              8s    {    
      
   __sig__136  |  |              8s                ~                   }                                         GetV tion           #   Compute the SemiDecomposition of M. dL  |L                           t                                        ~  ~  8s   ~  LP    
      
   __sig__123  <Q  TQ              8s  ~              $S             SemiDecomposition   U  0U                   ~                                      #   Compute the SemiDecomposition of M. HZ  `Z                               t                                  ,~  $~  8s  ~  ^    
      
   __sig__124  D`  \`              8s   ~              a          A   Compute the SemiDecomposition of the subspace Vdual inside Mdual.   Xf  pf                               t    t                            <~  4~  8s  (~  ,k    
      
   __sig__125  l  l              8s  0~              o          S   Compute the SemiDecomposition of the subspace Vdual inside Mdual, starting with Tp. xv  v                                   t    t                          D~  8s  8~  y    
      
   __sig__126  z  z              8s  @~              @|    
      
   __sig__127  P}  d}    
      
   DecompFast                       8                                                                                             T  8s      `    
      
   __sig__139  X  p          4 8s  P  X                                                                                 `  8s          
      
   __sig__140    $          4 8s  \  X            t    
         LabelHelper   <                   X                                         Print   x          O   Label the factors in the decomposition D, then return the sorted decomposition. !   "  "                                                                       x  8s  l  H%    
      
   __sig__141  l&  &          4 8s  t  X            t(  )"                         t                                            8s      \-  +"            8s                |/  ,"           EllipticInvariants  0  1  -"                                               ."        .   Computes w1, w2, c4, c6, and j to precision n.  H5  /"                             t                                      Ĉ  8s    4:  0"  
      
   __sig__258  ;  $;  1"            8s                \<  2"        ,   Returns the abelian variety associated to A. >  >  3"                         t                                            Ԉ  8s  Ȉ  B  4"  
      
   __sig__259  D  D  5"            8s  Ј              ,G  6"  
         AbelianVariety  H  7"                 ̈                              8"  H        Computes an elliptic curve associated to the weight-two rational modular symbols factor A (this curve is well-defined up to isogeny). By the Shimura-Taniyama theorem the computed curve is correct (assuming correctness of our implementation of the algorithms). V  hW  9"                         t                                              8s    ([  :"  
      
   __sig__260  ]  ]  ;"            8s                _  <"                             t                           V           8s      8c  ="  
      
   __sig__261  d  e  >"            8s                g  ?"  
      	   LAnalytic   0i  Hi  @"                                               A"  &      y   Compute L(A,j) for j a "critical integer", i.e., one of the integers 1,...,k-1. Use at least n terms of the q-expansions.   u  u  B"                                 t                     V             8s    y  C"  
      
   __sig__262  y   z  D"            8s                X{  E"                             t                           V       ,    8s      p~  X"           DerivG2 0             SignWN                                                                                                                       ,  8s          
      
   __sig__137                  8s  (                  
         DecompWq                        $                                                          t                                 L  @  8s      \    
      
   __sig__138    ,          4 8s  <  X              /   *         Give the subspace A of the DUAL of M, attach necessary data to make it a factor of M. For this to make sense, A should be Hecke stable. 	  	  <
  0                          t    t                           t         Ȁ  8s      2             8s  Ā              4  @            DecompZ    3                              t                                      Ԁ  8s        4   
      
   __sig__160      5         4 8s  Ѐ  X              6   
         DecompFastTp     7                  ̀                              8                              t                                        8s      "  9   
      
   __sig__161  #  #  :             8s                L%  ;            DecompCharpolyTp &  &  &  <                                                =                          t                                 t             8s       .  >   
      
   __sig__162  /   0  ?             8s                1  "            8s  0              2  "                         t                                        P  @  8s      6  "  
      
   __sig__251   9  (9  "            8s  <              :  "  
         PeriodLattice   ;  "                 8                              "        V   Computes the complex period lattice associated to A using n terms of the q-expansions.  A  "                             t                                      X  8s  L  F  "  
      
   __sig__252  G  G  "            8s  T              XK  "                         t                                 V       t  d  8s      hO  "  
      
   __sig__253  hP  P  "            8s  `              Q  "  
      
   RealVolume  S  S  "                 \                              "  .         Computes the volume of A(R), R the RealField. This function returns the volume of the identity component times the number RealTamagawa(A) of real components.   ]  "                             t                           V           |  8s  p  a  "  
      
   __sig__254  c  c  "            8s  x              e   "                         t                                 V           8s      Tj  !"  
      
   __sig__255  k  Hl  ""            8s                n  #"  
         ImaginaryVolume p  $"                                               %"        8   Computes the volume of A(iR), the pure imaginary points. x  x  x  &"                             t                           V             8s    {  '"  
      
   __sig__256  |  |  ("            8s                ~  *"  
      
   __sig__257     4    
         LabelFactors                      p                                                      t                                           8s      L%    
      
   __sig__142  p&  &          4 8s    X            x(                                                            Print the factors in D. -  -  -                                                                     8s    1    
      
   __sig__143  2  2          4 8s    X            4              newform s           8   Return the number of new factors of the decomposition D. 9  9  9                                                                         8s    <    
      
   __sig__144  =  =              8s                ?              NumNewformFactors                                                                                                                   t           (  8s        	   
      
   __sig__149      
             8s  $                                                                 #            Factor       D         Returns the modular factor "Nk[Weight][IsogenyClass]", where N is the level, k is the weight, and [IsogenyClass] is a letter such as "A", "B", etc. An alternative input format is "N[IsogenyClass]" in which case the weight is assumed to be two.                                                                t       L  @  8s  4  H#     
      
   __sig__150   $  X$               8s  <              $&     
         ModularFactor   '                    8                                                                                     t       X  T  8s      L/     
      
   __sig__151  0  0               8s  P              2                                                           t       d  `  8s      H5     
      
   __sig__152  6   7               8s  \              9                                t                           t       t  l  8s      \<     
      
   __sig__153  \=  t=               8s  h              x?     >         Returns the index into the D list of the new factor with the indicated isogeny class. If the iso classes have not yet been computed yet, they are computed. If there is no factor of class iso this function returns 0. TJ  J  TK                                                           t           |  8s  p  dO     
      
   __sig__154  dP  |P               8s  x              Q                                 t                           t           8s      V  !   
      
   __sig__155  W  X  "             8s                Y  $                                                %                              t                           t           8s      `  &   
      
   __sig__156  a  a  '             8s                Hd  (                                                         t           8s      Hi  )   
      
   __sig__157  hj  j  *             8s                l  +   >         Returns the index into the D list of the new factor with the indicated isogeny class. If the iso classes have not yet been computed yet, they are computed. If there is no factor of class iso this function returns 0. <y  Py  hy  ,                                                         t           8s    @|  -   
      
   __sig__158  P}  d}  .             8s                ~  1   
      
   __sig__159        
         NumOldFactors   A                                                         .   Return the indexes of new factors in the list.  G                                                                         8s    ,M    
      
   __sig__145  N  O              8s                |P    
      
   NewFactors  Q  Q                                                         .   Return the indexes of new factors in the list.  hW                                                                         8s    ([    
      
   __sig__146  ]  ]              8s                _    
         NewformFactors  `                                                         8   Return the number of new factors of the decomposition D. g  g  g                                                                         8s    k    
      
   __sig__147  m  m              8s                (p      
         NumNewFactors   t                                                           8   Return the number of new factors of the decomposition D. y  y  y                                                                          8s    ||     
      
   __sig__148  x}  }               8s                  K   
      	   CuspOrder       L                                                 M          e   Compute the order in A of the difference (x)-(y) of the cusps defined by the 2-tuples alpha and beta.     N                                  t                              @  8s  4    O   
      
   __sig__165      P             8s  <              t              LRatio tion Q   $      q   Computes the following upper bound on the torsion subgroup of A: gcd { #A(F_p) : 3 <= p <= 19, p not dividing N }       R                          t                                         `  P  8s  D  8!  S   
      
   __sig__166  0"  X"  T             8s  L              #  U   
         TorsionBound $  $  V                  H                              W   $      s   Computes the following upper bound on the torsion subgroup of A: gcd { #A(F_p) : 3 <= p <= maxp, p not dividing N } -  -  X                              t                                      h  8s  \  1  Y   
      
   __sig__167  2  2  Z             8s  d              h4  c   
      
   __sig__169 dMap x5  [   b      h  Compute the rational period mapping. The period mapping is scaled so that the integral modular symbols SkZ are taken surjectively onto the lattice Z^d. Note: the choice of rational period mapping is well-defined only once A is created, and can be different if A is created again; i.e., it is with respect to the non-canonical basis used internally to define A. D  D  D  \                          t                                 w           x  8s  l  I  ]   
      
   __sig__168  K  L  ^             8s  t              |M  _            ScaledRationalPeriodMap O  `                  p                              a         I   Compute the order in A of the cusp defined by X^i*Y^{k-2-i}*{alpha,beta}.   XU  U  b                                      t                            8s    Y  d             8s                |[  e                          t                                  8           8s      ,`  f   
      
   __sig__170  Pa  pa  g             8s                c  h   
         ModularKernel   Le  i                                                j   B         Compute the modular degree of A. This is the degree of the canonical map from the dual of A to A. When A corresponds to an elliptic curve, this is the SQUARE of what is frequently referred to as the "modular degree" in the literature.  xv  v  k                          t                                 8             8s    y  l   
      
   __sig__171  z  z  m             8s                @|  n   
         ModularDegree   d}  o                                                r   
      
   __sig__172    ,  A                                                B                          t                                 t             8s      
  C   
      
   __sig__163  x    D             8s                  E   
         DecompZdual     F                                                G         2   Compute the order in A of the difference (0)-(oo).  <  T  H                          t                                        8  (  8s    ,  I   
      
   __sig__164      J             8s  $              h           9   Return the level M of the character group of X_0(pM)/F_p.                                                                               8s    
     
      
   __sig__186                   8s                 4     
         XGroup_M     4                                                     >         Compute the n-th Hecke operator on the toric part (+Eisenstein series) of the closed fiber of the Neron model of J_0(pM) over F_p. The second argument returned is a diagonal matrix which is double the weight vector. |                                                                            8s    "     
      
   __sig__187  4#  L#               8s                $  i!                         u    u                                       8s    x(  k!            8s                *  m!                                               |!  
      
   __sig__223 iety /  n!        ;   Returns the dimension of the abelian variety attached to A. (2  @2  o!                         t                                            ą  8s    |5  p!  
      
   __sig__221  7  d7  q!        4 8s    X             9  r!           DimensionAbelianVariety (;  s!                                               t!  f      x  Attempt to compute the q-expansion of one of the Galois conjugate modular forms associated to A. This function uses theta series, so if successful it can be used to compute a very large number of Fourier coefficients quickly. If there is no prime which exactly divides Level(A), Weight(A) gt 2, the character of A is nontrivial, then the function qEigenform(A,prec) is called. M   N  N  u!                             t                           #          ܅  8s  Ѕ  Q  v!  
      
   __sig__222  S  S  w!            8s  ؅              U  x!  
         qEigenformTheta lW  y!                 ԅ                              z!        5   Returns the at least 7 terms of the q-expansion of A.    ]  {!                         t                                 #          8s    <a  }!            8s                <c  ~!  
      
   qEigenform  d   e  !                                               !         f   Returns the q-expansion of one of the eigenforms associated to A, computed to precision at least prec.  m  !                             t                           #            8s     u  !  
      
   __sig__224  |v  v  !        4 8s    X   4         x  R"           DerivG1 ts  !  *         Returns generators for the saturation of the Z-module generated by the sequence of q-expansions. Uses the smallest degree as precision. }  }  }  !                                                                       8s      ^"           DerivG3 ԁ  p   .         Returns the congruence number r = [S_k(N,Z) : (This) + (Complement)], along with the structure of the quotient; q-expansions are computed to precision prec. %  %  q                              t                            8           ́  8s    )  s             8s  ȁ              \,  t   
         CongruenceR -  -  u                  ā                              v   8         Computes the invariants of the group-theoretic intersection of the abelian varieties corresponding to the modular factors A and B. If the factors are not distinct, then the 0 group is returned.    9  (9  w                          t    t                           8           8s  ؁   <  x   
      
   __sig__173  <   =  y             8s                >     B         For an integer s in the critical strip (1<=s<=k-1), return the quotient L_A(s)*(s-1)! / (2pi)^(s-1)*Omega, which is a rational number. Here Omega is the volume of A(R), if s is odd, and the volume of the -1 eigenspace for conjugation.                                    t                                      P  8s  D       
      
   __sig__178  (                 8s  L                            B dED ing            T   Returns the odd part of the rational part of L(A,s); potentially faster than LRatio.                               t                                        l  `  8s  T  8!     
      
   __sig__179  0"  X"               8s  \              #     
         LRatioOddPart   $                    X                                                            t                                      t  8s       ,     
      
   __sig__180  -  -               8s  p              /               Returns true iff L(A,eps,1) = 0. 1  1  1                                t                                        8s  x  5     
      
   __sig__181  6  6               8s                9              LEpsilonVanishes :  :  :                    |                                       <   Returns the degrees d dividing p-1 such that L(A,eps,1) = 0. ?  x?                            t                                              8s    \D     
      
   __sig__182  TE  lE               8s                G              LEpsilonVanishing   0J  TJ                                                              TM  M  N     
         Z  [  2   5  \              prec SX   "      i   Return the character group X of the toric part of the closed fiber of the Neron model of J_0(p) over F_p.   U  V                                                                    Ԃ  Ă  8s    `Z     
      
   __sig__183  [  [               8s                ]              XGroup  d_                                                     .         Return the character group X of the toric part of the closed fiber of the Neron model of J_0(pM) over F_p. [RIGHT NOW RETURNS THE EISENSTEIN PART AS WELL.] i   j                                                                  t  ܂  8s  Ђ  Po     
      
   __sig__184  p  pq               8s  ؂              u           B   Return the characteristic p of the character group of X_0(pM)/F_p.  x  x                                                                          8s    {     
      
   __sig__185  |  |               8s                ~     
         XGroup_p     0                                                              TXn     z            AbelianIntersection pA  A  {                  ܁                              |         L   Returns the group-theoretic intersection of a sequence S of modular factors. H  I  }                                                           8             8s    M  ~   
      
   __sig__174  O  O               8s                $Q     8         Compute "[Phi(SkZ^+):Phi(W)]". If Plus is false, compute instead "[Phi(SkZ^-):Phi(W)]". It should be the case that W tensor Q is contained in SkZ^+ tensor Q (or SkZ^- tensor Q, when Plus is false).   0Z                                t    t                                  8s     ^     
      
   __sig__175  _  ,`               8s                a     
         PeriodIndex c  c                                                           P   Returns the lattice spanned by the basis of W under the period map defined by A. k  Pk  hk                            t    t                                     $  8s    p     
      
   __sig__176  ,u  du               8s                 v     
         PeriodImage w  Dx                                                                            t                                        H  8  8s      |     
      
   __sig__177  }  }               8s  4              0                    0                                 
         PhiX_and_mX                       D                                       /   Returns the dimension of the character group X. 
  
  
                                                                        d  8s  X  `     
      
   __sig__190  P  h               8s  `                   
      
   XDimension    (                    \                                 6         Returns the character group of the toric part of the closed fiber at p of the space M of modular symbols. This only makes sense when p exactly divides the level of M and M has weight two.                                     t                                    |  8s  p  #     
      
   __sig__191   %  H%               8s  x              &     *         Returns the character group corresponding to the largest prime p which exactly divides the level. If no such p exists, an error results. -  .  .                            t                                              8s    2     
      
   __sig__192  3  43               8s                4           =   Compute XGroup for xmallest prime exactly dividing the level.   $9                            t                                 t           8s    ;     
      
   __sig__193  <  <               8s                >                                                     (         Return the factor of the character group corresponding to the p-adic rigid analytic optimal and co-optimal quotient associated to A. G  H                                t                           8             8s    |M     
      
   __sig__194  $O  dO               8s                P           ]   Compute the p-adic modular degree of A, at the largest prime which exactly divides the level.   0U                            t                                        ԃ  ă  8s    tY     
      
   __sig__195  Z  Z               8s                ]              PhiX ]  ^                                                            f   Compute the order of the image of the component group of J_0(N) in the component group of A, all at p.  pf                                t                                      ܃  8s  Ѓ  ,k     
      
   __sig__196  l  l               8s  ؃              o  l!           Dot ce or            Y   Compute the p-adic modular degree of A, at largest prime which exactly divides the level.   w  Dx                            t                                            8s    z     
      
   __sig__197  {   |               8s                d}     
         XModularDegree  ~                                                           '   Compute the p-adic modular degree of A. <  d                                                                XGroupV                Returns the monodromy weights.  	                                                                    P  4  8s  (       
      
   __sig__188                   8s  0                            MonodromyWeights                         ,                                       4   Computes the quantities PhiX and mX associated to V.                               8                                         L  8s  @       
      
   __sig__189                     8s  H              "  >!  .         Let T be an nxn matrix over K with irreducible characteristic polynomial f. This function returns an eigenvector for T over the extension field K[x]/(f(x)). 
  
  @!  
      
   __sig__212      A!        4 8s     X              B!  8         The elements of gens should all lie in a field Q[x]/(f(x)). It is assumed that they generate a subring O of Q[x]/(f(x)), as a *Z-module*! This function returns the discriminant of this Z-module.      C!                                                                       8s      D!  
      
   __sig__213  4  l  E!            8s                   F!  
         ZAlgDisc !  !  !  G!                                               H!  *         If A is newform modular factor, compute the discriminant of the ring generated by the Fourier coefficients of one of the q-expansions of A. )  )  I!                         t                                            ,  8s     /  J!  
      
   __sig__214  80  p0  K!            8s  (              1  L!  
         DiscriminantOf  2  M!                 $                              N!  *         If A is newform modular factor, compute the discriminant of the ring generated by the Fourier coefficients of one of the q-expansions of A. p;  ;  O!                         t                                            D  8s  8  >  P!  
      
   __sig__215  H@  x@  Q!            8s  @              B  R!  
         DiscriminantKf  D  S!                 <                              T!        K   Compute the motive B made from the *=sign subspace of the modular motive A. hL  L  U!                             t                           t           \  8s  P  PP  V!  
      
   __sig__216  @Q  XQ  W!            8s  X              (S  X!  
         SignedSubspace  T  Y!                 T                              Z!        +   Compute eigenvector for sign subspace of A. LZ  dZ  [!                             t                           u       |  t  8s  h  ^  \!  
      
   __sig__217  H`  ``  ]!        4 8s  p  X            a  ^!  $      p   Returns an eigenvector of the Hecke algebra on A over a polynomial extension of the ground field. A must be new. h  h  i  _!                         t                                 u             8s  x  m  `!  
      
   __sig__218  lo  o  a!        4 8s    X            ht  b!        Z   Returns the images of the ith standard basis vector under the Hecke operators Tp for p<=n.  x  x  c!                         t                                          8s    \{  d!  
      
   __sig__219  l|  |  e!        4 8s    X            }  f!  
         HeckeImages ~    g!                                               h!        #   Compute the dot product of v and w.   ̂  j!  
      
   __sig__220    ,                                t                                        8s    X&   !  
      
   __sig__198  @'  '  !            8s                 )  !        +   Computes the quantity PhiX associated to V. -  `-  !                         8    8                                         8s    P1  !  
      
   __sig__199  X2  p2  !            8s                <4  !        S   Returns the Mestre module of M. The level must be prime and the weight must be two.  9  (9  !                         t                                 8           $  8s     <  !  
      
   __sig__200  <   =  	!            8s                 >  
!  
         MestreGroup H@  x@  !                                               !  4         Return the factor of the character group corresponding (maybe) to the p-adic rigid analytic optimal quotient associated to A. The representation is via the Mestre construction. L  L   M  !                         t                                 8           <  8s  0  P  !  
      
   __sig__201  Q  Q  !            8s  8              T   !  L        Let v be a choice of eigenvector, corresponding to A, on the module of supersingular points. This function returns sum w_i (v_i)^n, a quantity which, by Gross-Zagier, is relevant to the computation of the order of vanishing of L(A,s) at 1. Currently Conductor(A) must be prime.     !!                             t                                       8s      #!            8s                  $!  (         Compute the order of the group of *geometric* points of the component group at the largest prime that exactly divides the level.   0  H  %!                         t                                            8s    !  &!  
      
   __sig__206  "  "  '!            8s                $  (!  
         ComponentGroup  %  )!                                               *!  :         Compute the order of the group of *geometric* points of the component group at p, assuming that p exactly divides the level. If working in the +1 quotient, then only the odd part of the order is returned. 1  1  +!                             t                                        8s    4  ,!  
      
   __sig__207   6  h6  -!            8s                $9  .!  :         Compute the order of the group of Fp rational points of the component group of A at the largest prime which exactly divides the level of A. WARNING: Stein has not yet nailed down the power of 2 when Wp=+1!   t@  /!                         t                                        Ȅ  Ą  8s    D  0!  
      
   __sig__208  F  F  1!            8s                H  2!                             t                                      Є  8s      M  3!  
      
   __sig__209  O  O  4!            8s  ̄              P  5!          Try to compute the odd part of the order of Sha. Assuming BSD we obtain a number which is either zero or divides the true order of Sha, and only misses primes where the representations are reducible. The following caveats apply: (a) We assume the BSD formula. (b) We use the upper bound on torsion coming from Hecke operators, so the result of this function might be too small. (C) At primes whose square divide the level we do not know how to compute cp; however such cp can only be divisible by p and primes dividing the order of the torsin group. We simply make our conjectural value of Sha coprime to such primes when there is a p whose square divides the level.  @n  Xn  6!                         t                                              8s  Ԅ  u  7!  
      
   __sig__210  v  v  8!            8s  ܄              x  9!                                                          u           8s      X{  :!  
      
   __sig__211  h|  ||  ;!            8s                }  <!  
         Eigenvector ~    =!                                               ?!                                                        u       l    8s    (  @  T  !  
         MestreGroupV V  XV  !                 4                              !                         t                                       \  P  8s      \]  !  
      
   __sig__202  ^  _  !            8s  L              `  !           MestreEigenvector   pb  b  !                 H                              !                         8    8                                     d  8s      Pj  !  
      
   __sig__203  k  Dl  !            8s  `              n  !  6         This function returns sum w_i (e_i)^n, a quantity which, by Gross-Zagier, is relevant to the computation of the order of vanishing of L(A,s) at 1. Currently Conductor(A) must be prime. y  Py  hy  !                             u    8                             t  8s  h  @|  !  
      
   __sig__204  P}  d}  !            8s  p              ~  !  
         MestrePowerSum    !                 l                              "!  
      
   __sig__205      !  
         SaturatePolySeq   !                                               !  ,         Returns the index and structure of the Z-module generated by the sequence of q-expansions in its saturation. Uses the smallest degree as precision.   0  !                                                                      4  8s  (    !  
      
   __sig__226  H  t  !            8s  0                !           IndexInSaturation   t    !                 ,                              !        
   __sig__228 ntegralBasis   !        M   Returns the linear combination of qIntegralBasis(A) which gives Eigenform(A).   "  !                         t                                 t           L  8s  @  H%  !  
      
   __sig__227  l&  &  !            8s  H              t(  !                             #   t                     V       ć    8s    \-  !            8s                |/  !           FastPeriodIntegral  0  1  !                                               !                             #   t                     V           ̇  8s      6  !  
      
   __sig__245  8  $9  !            8s  ȇ              :  !  <         Given a homogeneous polynomial P(X,Y) of degree k-2, a 2x2 matrix g=[a,b,c,d], and a q-expansion f of a weight k modular form, this function returns the period <f, P {oo,g(oo)}> = Int_{oo,g(oo)} P(z,1) f(z) dz.  HB  B  !                             #   t                     V           ܇  8s  Ї  \G  !  
      
   __sig__246  H  I  !            8s  ؇              LL  !           SlowPeriodIntegral  M  M  !                 ԇ                              !                             t                                         8s      T  !  
      
   __sig__247  XU  U  !            8s                W  !           PeriodGenerators X  HY  tY  !                                               !                         t                                        ,    8s      \`   "  
      
   __sig__248  a  a  "            8s                 d  "  
         PeriodMapping   e  "                                               "        (   Apply the period mapping Phi to v in Mk. k  k  k  "                         u                               u             8s    pq  "  
      
   __sig__249  |u  u  "            8s                v  "           ApplyPeriodMapping  x  x  	"                                               
"  :         Computes the complex period mapping associated to A using n terms of the q-expansions. The period map is a homomorphism Phi:Mk(N,eps;Q)--> C^d, where d=dim A. Furthermore, A(C) := C^d/Phi(Sk(N,eps;Z)).   ؀    "                             t                                      4  8s  (  (  "  
      
   __sig__250  `    !  
      
   __sig__225       !            8s                P  !  
      
   __sig__235      !            8s                  !  
      
   __sig__240 gation g !        3   Returns the map r_A : M_k(Q) ----> M_k(Q)/Ker(Phi). L  d  !                         t                                               8s      !  
      
   __sig__236      !            8s                  !           RationalPeriodMapping   X  !                                               !        E   Returns the map r_A : M_k(Q) ----> M_k(Q)/(Ker(Phi)+(sign quotient)).     !                             t                                        8s    |!  !  
      
   __sig__237  "  "  !            8s                #  !           SignedRationalPeriodMapping %  %  !                                               !        8   Returns a basis for the image of S_k(Z) in M_k/Ker(Phi). ,  <,  \,  !                         t                                            0  8s  $  0  !  
      
   __sig__238  1  1  !            8s  ,              83  !           RationalPeriodLattice   4  !                 (                              !        X   Returns matrix of "conjugation" with respect to the basis RationalPeriodLatticeBasis(A). ;  ;  ;  !                         t                                            H  8s  <  (?  !  
      
   __sig__239  @  @  !            8s  D              B  !           RationalPeriodConjugation   E  @E  !                 @                              !        N   Computes the number of real components of the abelian variety associated to A.  0M  !                         t                                            `  8s  T  P  !            8s  \              DR  !           ImaginaryTamagawa   T  T  !                 X                              !        N   Computes the number of real components of the abelian variety associated to A.  ,[  !                         t                                            x  8s  l  _  !  
      
   __sig__241  `  <a  !            8s  t              <c  !  
         RealTamagawa d   e  !                 p                              !        E   Computes <f, {alpha,oo}> for alpha any point in the upper half plane.   Hl  !                         V    #                          V           8s    q  !  
      
   __sig__242  u  u  !            8s                $w  !  
         PeriodIntegral  x  !                                               !        F   Computes <f, P{alpha,oo}> for alpha any point in the upper half plane.  |  !                         V        #                    V             8s      !  
      
   __sig__243      !            8s                  !           Compute <f, {oo, g(oo)}>.   D  X  !  
      
   __sig__244    ̅  !           EigenformInTermsOfIntegralBasis 
  !                 D                              !        J   Return an integral basis for the sum of the spaces in the decomposition D.      !                                                                 t  d  8s  X  X  !            8s  `                !  
         qIntegralBasis    !                 \                              !        S   Return an integral basis for the sum of the cuspidal spaces in the decomposition D. T!  |!  !                                                                 |  8s  p  \$  !  
      
   __sig__229  %  %  !            8s  x               '  !                         t                                            8s      \,  !  
      
   __sig__230  -  -  !            8s                 0  !  B         Compute an integral basis for the space spanned by the Galois conjugates associated to A. If A is a space of modular symbols, returns an integral basis for the corresponding space of cusp forms. The base field must be the rationals. 9  9  9  !                             t                                        8s    <  !  
      
   __sig__231  =  =  !            8s                ?  !        /   Compute the sum of two modular symbols factors. B  B  B  !                         t    t                           t             8s    G  !  
      
   __sig__232  I  I  !            8s                L  !  
      
   AddFactors  M  N  !                                               !  <         Compute the intersection of two modular symbols factors. If the intersection is zero-dimensional use the function "Intersection" to compute the structure of the corresponding intersection of abelian varieties.   Z  0Z  !                         t    t                           t             8s    ^  !  
      
   __sig__233  _  ,`  !            8s                a  !           IntersectFactors c  c  d  !                                               !  &      ~   Given a list polyprimes of pairs <p, f(x)> computes the following subspace of the dual of M: intersect ker(f(Transpose(Tp))).   m  !                             t                           t         ؆  8s  ̆  u  !  
      
   __sig__234  xv  v  !            8s  Ԇ              x  !  
         DualSubspace y  hy  !                 І                              !  <          Given a sequence polyprimes [<p1, f1(x)>,...<pr,fr(x)>] of pairs a prime and a polynomial, this function computes the following subspace of the subspace W of the dual of M: intersect ker(f(Transpose(Tp))).  Ё      !                             t    t                     t             8s      S"                 <                              T"        N   Compute the G_2 function defined in section 2.13 of Cremona's Algorithms book.    U"                         V                                 V           \  8s  P  0  V"  
      
   __sig__266  (  @  W"            8s  X                Y"                 T                              Z"        N   Compute the G_3 function defined in section 2.13 of Cremona's Algorithms book.  |  ["                         V                                 V           t  8s  h  h   \"  
      
   __sig__267  !  !  ]"            8s  p              #  _"                 l                              `"  6         Compute (d!)*Prod L^(dr)(fi,1) over the d Galois conjugates of f. TODO: When both r > 1 and d>1 the normalization is wrong! It's trivial combinatoric to work out but I have not done it.   -  -  a"                                 #                    V             8s    1  b"  
      
   __sig__268  2  2  c"            8s                4  d"  
         DerivWt2 5  5  5  e"                                               6#           T   5  ]  f"                         t                                 V           8s      <  g"  
      
   __sig__269  $>  >  h"            8s                t@  i"                             t                           V           8s      D  j"  
      
   __sig__270  F  F  k"            8s                H  l"  8         Return the leading coefficient of Taylor expansion about the critical integer j and the analytic rank of the the L-series associated to A. The precision used is at least n terms of the q-expansion.   Q  m"                                 t                     V              8s    V  n"  
      
   __sig__271  W  X  o"            8s                Y  x"  
      
   __sig__273 ield ([  p"  4         Returns two arguments, a v-adic field K and an element zeta in K that is a primitive pth root of unity. Here v should be a prime number, or 0; if v=0 then K=the complex numbers.   c  d  q"                                                                  ̉  8s    i  r"  
      
   __sig__272  8j  Pj  s"            8s  ȉ              tl  t"           CompleteCyclotomicField t  u"                 ĉ                              v"        >    Returns true iff the character eps is the trivial character.   y  w"                                                                       8s  ؉  |  y"        4 8s    X   (         }  z"        )    Returns the level of the character eps.        {"                                                                       8s      |"  
      
   __sig__274  D  X  }"        4 8s    X   ,           ~"        )    Returns the level of the character eps.        "        
   __sig__275  L  d  |    (           p1list      (           n e.m m m   (           Sgens ecform(           Squot   Df  (           Scoef   k  (           Tgens   `  (           Tquot   s  (             H                ģ            H    (  
         GetCategory ,{ خ (                                         <   x     $   x        x  	    x  0               (           M       (             ˸(            أ  0   ԣ     У        ܣ  (  ,      H    (  
         SetCategory gory;   (                                            |   P   |      $         |      |         D               (              (     ̣  ȣ      (           M eturn    (  
         category x    (              (             4     	              @          H    (  
         NormalizePair //////(                                                                                                    (        -   Bad x=%o, N=%o, u=%o, minv=%o, s=%o, mint=%o
  h (             N, u, minv, )                      $  (  ,  0  4  8  <  )           x $)           Z  4 <x )           u  Pl X )  
         v 1]; rRing(); x)  a)           R  7  )           N  8r     )           g  Z ! u; 0,)           s           	)           d  Я l 
)           minv        )           mint  $ )           Ng  p @s )           vNg 00     )           t *Ng; ; r )           k  Pl X )            ,W  )           L  l           P        H  h          H    )  
         P1Reduce , m0QhQ)                                         0      <      L        \                     $                                       	                                                     (    8         D     `  
            p  	      |                       	                                                                 d            <       H     X               	      0                  )     T  X  \  `  d  )           x //////////)           list        )  
         N 1Reduce(x, list)  )           n rn 0, 1;  )           s  Pl X )              )  
         EnumerateP1 c L >#                                                        8              8s    t~  ?#  
      
   __sig__312  H  h  @#            8s                  A#        K   Computes Tp on the Mestre graphs module. p must be a prime between 2 and 7.   ,  B#                             8                                        8s    h  C#  
      
   __sig__313  l    D#            8s                H  $           SlopeAlphaPartGamma0     $                                               $        4   Return the smallest valuation of a coefficient of f.     $                                                                             $                            0  $  
         SlopeValuation     $                                               $  
      	   __sig__21 ngruences $                                                                        #  $  
      	   __sig__20   $%  L%  $                            &  $           pAdicFamilySlopeCongruences 1  1  $                                               $                                                               В        t8  $              ̒              4:  $           pAdicFamilyTable ;  <;  T;  $                 Ȓ                              $        #   /home/was/magma/Startup/shortcuts.m '0$        #   /home/was/magma/Startup/shortcuts.m 0(0$           Fast, non-proved, charpoly. D  D  $                                                                           I  $  
         __sig__0 K  K  L  $                            |M  $  
         modcharpoly O  O  $                                               $           factor(charpoly(f)); S  S  $                                                                           X  $  
         __sig__1 X  LY  xY  $                            ,[  $                                                $           factormod, as in PARI   0`  $                                                                          Ld  $  
         __sig__2 e  e  Df  $                            h  $  
      	   factormod   i  $j  $                                               $            /home/was/magma/Startup/custom.m o  :@?<%  
         __sig__1       =  =%            ̔                    >%        .   Returns the Chinese remainder lift of a and b.     ?%                         r    r                           L           ̔    <?  @%  
         __sig__2       >  A%            ̔                     B%        .   Returns the Chinese remainder lift of a and b. 7    C%                         L    r                           L           ̔      D%  
         __sig__3 t6       E%            ̔                7F%        .   Returns the Chinese remainder lift of a and b.      G%                         r    L                           L       ,  $  ̔       H%  
         __sig__4 K         I%            ̔                 K  J%        1   Returns the Chinese remainder lift of the list A. 7       K%                        L                                 L           4  ̔  (  7L%  
         __sig__5       ,R  M%            ̔  0                  O%                                                                     D  ̔  8  @  Q%            ̔  @                  R%  
         IsSquareFree @  7S%                 <                              T%        +   Returns the quotient by the largest square.    @  U%                                                                     \  ̔  P      V%  
         __sig__7    @  7W%            ̔  X                 X%  
         SquareFreeRoot 7    Y%                 T                              Z%        ;   Returns the sequence of subsequences of [1..n] of length r. Pd      [%                                                                 t  ̔  h     \%  
         __sig__8 f         ]%            ̔  p              h  ^%        3   Returns the sequence of subsets of r elements of S.        _%                                                                  ̔  x  7`%  
         __sig__9       4s  a%            ̔                    c%                 |                              f%  
      	   __sig__10           $            /home/was/magma/Startup/custom.m    SxW'           a  b      $        J   The twist of E over the quadratic extension obtained by adjoining Sqrt(d).     ]  $                             |                           |           @  0  4      $  
         __sig__0     b      $            0  <                 $        '   /home/was/magma/Kohel/brandt_modules.mg xW$        '   /home/was/magma/Kohel/brandt_modules.mg xW$  (         Returns the sequences of sequences of Brandt modules of level N, for an maximal order in the algebra ramified at primes dividing N. i      $                                                                 h  X  H  L     $  
         __sig__0 p         $            H  T              4s  $  
         BrandtModules   0s  $                 P                              (  
               4     t(  (  
   \                      (  
         EchelonBasis    ?  (                 h                              (        2   /home/was/magma/Kohel/supersingular_polynomials.mg   hp(     
   2   /home/was/magma/Kohel/supersingular_polynomials.mg  php(  
         __sig__3 nomials @  (        )   Returns the gth supersingular polynomial.      I  (                                                                            (  
         __sig__0    L      (                               (        .   Returns the first g supersingular polynomials.  @  (                                                                             (  
         __sig__1    @  7(                               (           SupersingularPolynomials V         (                                               (        5   Returns the first g supersingular polynomials over R.   @  (                                                                            (  
         __sig__2    @  7(                               (        B   Returns the puiseux series expansion of the kth Eisenstein series.  7    (                                                                  Ȣ      @  (              Ģ                  (           EisensteinSeries 7       (                                               (        A   Returns the Petersson inner product of modular functions f and g.       k  (                                                                    Ԣ      (  
         __sig__4    Xq      (              ܢ                  (           PeterssonInnerProduct   7(                 آ                              (  
         LeftOrderForm     (                                               (        A   Returns the Gram matrix of the norm form of the right order of I.     (  (                                                                     (  |      	(  
      	   __sig__19       
(            |  $                (  
         RightOrderForm    (                                                (        O   Returns the Gram matrix of the norm form of basis B for the quaternion ideal I.       (                                                                   @  |  4  x!  (  
      	   __sig__20   "  "  (            |  <              #  (  
      	   BasisForm    %  H%  (                 8                              (        +   Returns the left ideal of A generated by M. *  *  (                                                                   X  |  L  |/  (  
      	   __sig__21   0  0  (            |  T              <2  (  
      	   LeftIdeal   P3  h3  (                 P                              (        ,   Returns the right ideal of A generated by M. 9  9  (                                                                   p  |  d  ,<  (  
      	   __sig__22   =  ,=  (            |  l              $?  (  
      
   RightIdeal  @  @  (                 h                              (        !   Returns the conjugate ideal of I.   F  F   (                                                                       |  |  L  !(  
      	   __sig__23   M  ,M  "(            |                dO  #(  
         IdealConjugate  |P  $(                                               %(  "      k   Returns the composite I*J in A, where I and J are respectively right and left ideals in the same algebra A. X  4X  &(                                                                     |    \  '(  
      	   __sig__24   ]  ]  ((            |                ,`  )(  
         IdealComposite  pa  *(                                               +(         _   Returns the composite Conjugate(I)*J in A, where I and J are left ideals in the same algebra A. i  i   j  ,(                                                                     |    Po  -(  
      	   __sig__25   p  pq  .(            |                u  /(           LeftSkewComposite   v   w  0(                                               1(         `   Returns the composite I*Conjugate(J) in A, where I and J are right ideals in the same algebra A. |  |  |  2(                                                                   Р  |  Ġ    3(  
      	   __sig__26   ؀    4(            |  ̠              <  5(           RightSkewComposite    ȃ  6(                 Ƞ                              7(        C   Returns the ideal of A generated by elements of the form x*y - y*x.   ؈  8(                                                                       |  ܠ    9(  
      	   __sig__27       :(            |                Ԏ  ;(            Returns the suborder Z + P in A.     Ȑ  <(                                                                     |      =(  
      	   __sig__28     H  >(            |                  ?(         a   Returns an element of A whose coordinates in terms of the reduced basis are random elements of I.       @(                                                                     |    <  (        @   Returns the Gram matrix of the norm form of the left order of I. 
    (  (                                                                       |      (  
      	   __sig__18       (            |                  '            |  $                '           Returns the reduced trace of x. t      '                                                                    8  |  ,    '  
         __sig__8   0  h  '            |  4                 '  
         ReducedTrace !  !  '                 0                              '           Returns the reduced norm of x.  %  '                                                                    P  |  D  T)  '  
         __sig__9 +  +  +  '            |  L              -  '  
         ReducedNorm d/  |/  '                 H                              '  
      	   __sig__11 nomial 2  '        J   Returns the characteristic polynomial of the quaternion algebra element x.   6  h6  '                                                                    h  |  \  :  '  
      	   __sig__10   ;  ;  '            |  d              <  '        A   Returns the conjugate of x as an element of a quaternion algebra.   @  @  '                                                                     x  |  l  <E  '            |  t              \G  '        @   Returns the bilinear product of x and y in a quaternion algebra. L  dL  |L  '                                                                    |  |  LP  '  
      	   __sig__12   <Q  TQ  '            |                $S  '  
         BilinearProduct T  '                                               '        P   Returns true if the quadratic form of B1 is smaller than that of B2, else false. [  [  [  '                                                             ȡ    |    \`  '  
      	   __sig__13   a  a  '            |                d  '        ,   Returns the commutator x*y - y*x of x and y. g  g  '                                                                     |    k  '  
      	   __sig__14   m  m  '            |                (p  '  
      
   Commutator  |t  t  '                                               '        C   Returns the Gram matrix of the norm form of a quaternion algebra R. y  y  '                                                                     ȟ  |    |  '  
      	   __sig__15   }  }  '            |  ğ              0  '  
         NormForm     ,  '                                               '         _   Returns the Gram matrix of the norm form of the quaternion ideal I, followed by the ideal norm. 8  P  h  '                                                                       |  ԟ    '  
      	   __sig__16   X  p  '            |  ܟ                '  
      	   IdealForm   č    '                 ؟                              '         _   Returns the Gram matrix of the norm form of the quaternion ideal I, followed by the ideal norm. Ԓ      '                                                                       |      '  
      	   __sig__17   @  X  '            |                  '  
         ReducedForm      (                                               '                         o    |                           |           l    `  X"  '              h              #  '  
         VeluImageCurve  $  '                 d                              '        ,   /home/was/magma/Kohel/quaternion_algebras.mg '     F   ,   /home/was/magma/Kohel/quaternion_algebras.mg '  
         inclusion_map   |/  '  
         reduced_basis   0  '        :   Returns the inclusion map of I in its left or right order.  P3  h3  '                                                                       |    `7  '  
         __sig__0 9  9  9  '            |                :  '           Returns the left order of I. <  \<  '                                                                       |    ,@  '  
         __sig__1 A  pA  A  '            |                \D  '  
      
   IdealOrder  TE  lE  '                                               '        )   Returns the reduced basis of the ideal I.   dL  |L  '                                                                       |    LP  '  
         __sig__2 Q  <Q  TQ  '            |                $S  '  
         ReducedBasis T  T  '                                               '  B         Returns the associative algebra over the integers defined by generators x and y, where Z[x] and Z[y] are quadratic suborders of discriminant D1 and D2, respectively, and Z[x*y - y*x] is a quadratic suborder of discriminant D1*D2 - T^2. a  a  '                                                                ؞  |  ̞  4g  '  
         __sig__3 h  h  i  '            |  Ԟ              j  '           QuaternionAlgebra   l  l  '                 О                              '  
         __sig__5 bra t  t  '        A   Returns the quaternion subalgebra generated by the elements in S.   w  Dx  '                                                                     |    z  '  
         __sig__4 {  {   |  '            |                d}  '           QuaternionSubAlgebra ~  ~  '                                               '  "      n   Returns a quaternion algebra of reduced discriminant N*M, ramified at infinity and at the prime divisors of N.    '                                                                   |      '            |                  '  "      l   Returns a quaternion algebra of reduced discriminant N, ramified at infinity and at the prime divisors of N.     '                                                                       |      '  
         __sig__6     $  '            |                \  '        (   Returns the reduced discriminant of the    8  L  '                                                                     (  |    h  '  
         __sig__7       (           x   8  P  Y           <          $  L  d  |    H     X          T                	  (	  @	  X	  p	  	  	  	  	  	  <
  d
  
  
  
  
  
    ,  L  d  |            ,  D  \  t                4  L  d  |              4  T  l              ,  D  d                    ,      ,  L  x        (  @  X  p      x           0  x           @  `  x      @  p          0  x    0  H  `                     4  L  d  |      4  l          t        $   l               !  <!  T!  |!  !  !  !  !  "  "  4"  \"  "  "  "  "  #  #  4#  L#  d#  |#  #  #  #  #  #  $  $$  \$  $  $  $  $  $%  L%  t%  %  %  %  %  (&  @&  X&  p&  &  &  &  &  &   '   '  @'  '  '  '  ((  x(  (  (  )  ()  @)  X)  )  )  )  *  *  *  D+  +  +  +  ,  $,  <,  \,  |,  ,  ,  ,  -  `-  -  -  -  -  .   .  .  /  (/  P/  h/  /  /  /  /   0  80  p0  0  0  0  0  0  1  81  P1  1  1  1  1  1  2  (2  @2  X2  p2  2  2  2  2   3  83  T3  l3  3  3  3  <4  T4  l4  4  4  4  4  4  5  ,5  L5  d5  |5  5  5  $6  l6  6  6  6  7  7  d7  7  x8  8  8   9  (9  @9  9  9  9  9  9   :  8:  P:  h:  :  :  :  :  :  :  ;  (;  @;  X;  p;  ;  ;  ;  ;   <  <  0<  H<  `<  x<  <  <  <  <   =  =  0=  `=  x=  =  =  =  =  (>  >  >  >  ?  (?  \?  |?  ?  ?  @  0@  H@  x@  @  @  @  @  A  (A  tA  A  A  A  A  B  LB  B  B  B  DC  |C  HD  `D  xD  D  D  D  D  D  E  @E  XE  pE  E  F  F  F  F   G  G  0G  HG  `G  xG  G  G  G   H  H  pH  H  H  I  I  I  4J  XJ  J  XK  K  K   L  L  8L  PL  hL  L  L  L  L   M  M  0M  hM  M  M  M  M  M   N  N  N  O  (O  hO  O  O  O  O   P   P  8P  PP  hP  P  P  P  P  P  Q  (Q  @Q  XQ  Q  Q  Q  Q  Q   R  R  DR  R  R  R  (S  S  S  S  T  $T  xT  T  T  T  T  U  4U  \U  U  U  U  U  V  ,V  \V  pV  V   W  lW  W  W  W  X   X  8X  PX  lX  X  X  X  X  LY  xY  Y  Y  Z  4Z  LZ  dZ  xZ  Z  Z  Z  [  ,[  P[  [  [  [  \   \  h\  \  ]   ]  H]  `]  x]  ]  ]  ]  ]  ^  d^  ^   _   _  D_  h_  _  _  _  0`  H`  ``  x`  `  `  `  `  <a  Ta  ta  a  a  a  a  a  \b  tb  b  c  <c  c  c  c  d  4d  Ld  d  d  d   e  8e  Pe  he  e  e  Df  \f  tf  f  8g  g  g  g  g   h  Xh  ph  h  h  i  4i  Li  ti  i  i  i  i  $j  <j  Tj  lj  j  j  0k  Tk  lk  k  k  k  Hl  `l  xl  l  l  l  m  m  m  Dn  \n  n  n  o  To  lo  o  o  o  p  ,p  p  p  p  tq  q  q  r  ht  t  t  0u  hu  u  u  u  u  u  v  v  0v  Dv  Xv  |v  v  v  v  v  $w  Dw  w  w  w   x  Hx  lx  x  x  x  x  x  y  y  ,y  @y  Ty  ly  y  y  y  y  y  z  z  ,z  @z  Xz  pz  z  z  z  z  {  ({  \{  {  {  {  {  {  |  ,|  D|  l|  |  |  |  |  |  $}  <}  T}  h}  |}  }  }  }  }  ~  \~  t~  ~  ~  ~  ~  ~       4  H  h                0  H    ܀        0  X        ԁ      ,  @  h      ̂      $  <  T  l    ̃    ,  D  X  |        4  L  d      ̅      $  <  T  l    Ȇ         8  P  h              $  H  l      ܈     $  L  d  |    ԉ    4  H  `  x    (  \  t      ̋        @  T  l        Ȍ      0  H  p      ȍ        ,  D  \  p        ؎      0  X            ,  D  l        ̐      (  @  t        ԑ      (  @  T  h        Ē  ؒ      (  `      ؓ      8  l          L  d         <  P  h            $  <  d      ܗ    ,  D  \      Ę  ܘ      $  <  T  l      ԙ    4  L  d  |      Ě      4  \  ̛  <  T  l        4  L  d  |      ܝ    H  \  t    Ȟ      @  X      П         0  H  `  x        ؠ     8  P  h          (  @  `  x    Т    Z           8             H  `  x    D    T          P                	  $	  <	  T	  l	  	  	  	  	  	  8
  `
  
  
  
  
  
    (  H  `  x            (  @  X  p                 0  H  `  x              0  P  h              (  @  `                    (      (  H  t        $  <  T  l      t          ,  t          <  \  t      <  l          ,  t    ,  D  \  |                  0  H  `  x      0  h          p            h               !  8!  P!  x!  !  !  !  !   "  "  0"  X"  "  "  "  "   #  #  0#  H#  `#  x#  #  #  #  #  #  $   $  X$  $  $  $  $   %  H%  p%  %  %  %  %  $&  <&  T&  l&  &  &  &  &  &  &  '  <'  |'  '  '  $(  t(  (  (  )  $)  <)  T)  )  )  )  *  *  *  @+  +  +  +   ,   ,  8,  X,  x,  ,  ,  ,  -  \-  -  -  -  -  .  .  .  /  $/  L/  d/  |/  /  /  /  /  40  l0  0  0  0  0  0  1  41  L1  1  1  1  1  1  2  $2  <2  T2  l2  2  2  2  2  3  43  P3  h3  3  3  3  84  P4  h4  4  4  4  4  4  5  (5  H5  `5  x5  5  5   6  h6  6  6  6   7  7  `7  7  t8  8  8  8  $9  <9  9  9  9  9  9  9  4:  L:  d:  |:  :  :  :  :  :  ;  $;  <;  T;  l;  ;  ;  ;  ;  ;  <  ,<  D<  \<  t<  <  <  <  <  <  =  ,=  \=  t=  =  =  =  =  $>  >  >  >  ?  $?  X?  x?  ?  ?  @  ,@  D@  t@  @  @  @  @   A  $A  pA  A  A  A  A  B  HB  B  B  B  @C  xC  DD  \D  tD  D  D  D  D  D  E  <E  TE  lE  E  F  F  F  F  F  G  ,G  DG  \G  tG  G  G  G  G  H  lH  H  H  I  I  I  0J  TJ  J  TK  K  K  K  L  4L  LL  dL  |L  L  L  L  L  M  ,M  dM  |M  M  M  M  M  M  N  N  O  $O  dO  O  O  O  O  O  P  4P  LP  dP  |P  P  P  P  P  Q  $Q  <Q  TQ  Q  Q  Q  Q  Q  Q  R  @R  R  R  R  $S  S  S  S  T   T  tT  T  T  T  T  U  0U  XU  U  U  U  U  V  (V  XV  lV  V  V  hW  W  W  W  X  X  4X  LX  hX  X  X  X  X  HY  tY  Y  Y  Z  0Z  HZ  `Z  tZ  Z  Z  Z  [  ([  L[  |[  [  [   \  \  d\  \  ]  ]  D]  \]  t]  ]  ]  ]  ]  ^  `^  ^  ^  _  @_  d_  _  _  _  ,`  D`  \`  t`  `  `  `  `  8a  Pa  pa  a  a  a  a  a  Xb  pb  b  c  8c  c  c  c  d  0d  Hd  d  d  d  e  4e  Le  de  e  e  @f  Xf  pf  f  4g  g  g  g  g  h  Th  lh  h  h  i  0i  Hi  pi  i  i  i  i   j  8j  Pj  hj  j  j  ,k  Pk  hk  k  k  k  Dl  \l  tl  l  l  l  m  m  m  @n  Xn  n  n  o  Po  ho  o  o  o  p  (p  p  p  p  pq  q  q  r  dt  |t  t  ,u  du  |u  u  u  u  u  v  v  ,v  @v  Tv  xv  v  v  v  v   w  @w  w  w  w  w  Dx  hx  x  x  x  x  x   y  y  (y  <y  Py  hy  y  y  y  y  y   z  z  (z  <z  Tz  lz  z  z  z  z  {  ${  X{  {  {  {  {  {   |  (|  @|  h|  ||  |  |  |  |   }  8}  P}  d}  x}  }  }  }  }  ~  X~  p~  ~  ~  ~  ~  ~      0  D  d  |               ,  D    ؀         ,  T  |      Ё      (  <  d      Ȃ         8  P  h    ȃ    (  @  T  x        0  H  `      ȅ         8  P  h    Ć  ܆      4  L  d  |               D  h      ؈       H  `  x    Љ    0  D  \  t    $  X  p      ȋ  ܋      <  P  h        Č      ,  D  l      č         (  @  X  l        Ԏ      ,  T  |          (  @  h        Ȑ      $  <  p        Б      $  <  P  d  |        Ԓ      $  \      ԓ      4  h          H  `        8  L  d  |             8  `      ؗ    (  @  X        ؘ         8  P  h      Й    0  H  `  x             0  X  ț  8  P  h        0  H  `  x      ؝    D  X  p    Ğ  ܞ    <  T      ̟        ,  D  \  t        Ԡ    4  L  d          $  <  \  t    ̢    (                                    D            E  
     P    <        < (                 B  (  
         charpoly     $A  (  
                         (           factor ȷ(  
   x                      (           isprime (  
   p                    (           matdet h(  
                         (           det X    (  
                         (  
                         (           msym irichle(  
           	              (           mf     Modu(     SetLogFile("valentine.log");    ʸ(  
           
              [                 1\  
                       /\              3\                 [                 [  
                   E  E  [                  IL                 R                 R                     R                          1     `1 4K     (K $K                      K K                         R                                         <K                                                             1L                     R                    R                     R                                     J                                 0 J                         R                 R                                               K                                                            R                                              J                     J 0                                R                     R                                                                  J                                         R                     !L              J                                                     J                                    R                                                                          J                               R               r                                                                 `0                        R                                                                                      J                   R                   R              q                                                                             tJ            L                    R                                                                                                      \0 ,  [              `.              q         p                                                               [                        p                                                          q                   [                       q             <q                                 8q Pq                         3[                                  p                     @q                                     p p     [                              p     \q q     q                                                         [  
               (o     R  
                   ;o,n 8\                 )\                 [                  [                 [                     [  
               o ʸ[                  [                     (  
         valentine.log (     M148:=ModularSymbols(DirichletCharacter(148,[1,6]),2,+1); B                   (           R ʸC     [       8 @       cke.dat arac(              -]  
   Hn                     (        L              (           /home/was/magma/Hecke/hecke.m       (  l     g        &    6  $  Y     3  
      /          m     (       +           7                       
  n          e  d      a  >         9  
         
    .          A       %   D            ;                  	  ]  [    
        .  0         9  B  a  B  &  ?  =    2    8    
             ;    a    >  L  %    
        @           1  #  $  7        (  '  "  ,  !  -  *  +  '      ,  )  /       W  c    6     `  K    E  ^  D  B  N  R    H  z  :      &  R    K  U  %  J  A  U  `  2  8  P     7  S    4  _  T  8    
  
    
  4  C  V  X  Y  ]  \  5  L    <  c  d  J  e  b    &  f              k  ?  l    |  j  m                    F  n  p    @      s  ]  M  3   w    v  x  z  {  u  y  t      |    }  ~  g        G        O             Z  c        =      Q          b            f            	    3            G      <      L           |                                      Z  i  [  i        F      E    h            E                                         <        $    
            	      0                   E           n       E            L  E            0                             
 
 E           InitialPrimes 8BʸE  `                                                 $                         p          |       D       4   
 `                                                                  !             "                      X                    
 	      L              E             E           n   D`  \`  E           p eqEnum ]  E           prmseq  x  E           i       E               E             0           $        4         
 
 E  
      
   PrimesUpTo e(p);   E  \                                                 $                         p          |       D       (   
 `             	          #                                    !             "                        H                 
 	      <              E     ( , 0 E           n       E           p num   h  E           prmseq    E             E           @ h           D       < T         
 
 E  
         Prime  q; me(p);   E  \                                       0        <     #                 	      L          $   X                                                                                   "                       D                   
 	      8                  E     H L P E           n   L  T  E           p rn 0;    E           i        E            $   E           ` P   d    h       \ |         
 
 E  
      
   IsLessThan e(p);   E                                        0      @        $               $        p        |                            	              
                                               	     	               ,     <           H       T     d                       	     	 t                                       d           
 	                        E                                     E     l p t x     E           u      $  E           v       E           n       E           i       E            D  E            @                        
 
 E           MySort ;   E  p                                      0    	            x    $         `       l                       	      |                       
                                                            	                    	     	 ,           8                H        t    T      `              #      )     %                                                                               d          $    <   	                 X                  &     "         )     (          ,                                                                             x          8    P   	                 l              p                                                             (       # 8                      X   &    d   )  t   (          ,       /     .      L         %                        	                    %        T                   ,       8       D                         &                          
 	                        E        	         
         
         	          	F        .   /home/was/magma/Kohel/elementary_arithmetic.mg  MySodF        T	             eF        p          fF  
                7       E                 E           B   ԉ  ؉  E           n      $  E           i   2  2  E           B1 n     E           i   T	  l	  E           B2  O  O  E           j ySort([ B[E           i ..n] ]);  E            E            @        	                
 
 E  
         ExteriorModule ]);  E                                         0     '           p     $          `     (                T               )                                                                       `             $       0       <   !    H   # * X        + h         (   &                       "       %                ,                                  	    t                           D              T   &          &                   -          	      t              E  
                           E        h
         nor E               E           L   S  T  E           r   d\  \  E           R s the lattE           M       E           n    ,   ,  E  
         S mension(L);   P  E           I2  t%  %  E           I1  4  l   F           N bsequencesF              F            @       (        l         
 
 F  
         ExteriorProduct F                                        0     '           p     $          `     )                T                      .                            "        "       #        $       #         #   (   !              4   ' /            P   
     \   
   h       t                               D                                                                      + (         H      @   (    L   +       '             t    	                                     0                    h              " 	   4         5       8       4               /          d          0    t                x      
        )       ,      (                /      1     0         '         
                                                  (               D        \                                 +                     2 
               "       %         (       ,                                  ,      8         ;      5    l  T              x                                    -          	                    F                                                                       F                                  <                  zF        H        B        
F     , 0 4 8 < @ D H L P T X \ ` d h     F           L   S  S  F           v   \   \  F           r   `
  
  F           R or power  F           n   -  -  F           V   ;  $;  F           x   HY  tY  F           B pace(R,n);F           j   LX  hX  F           i   K  L  F           M   $  $  F           T   h/  /  F           S       F           I2  -  -  F           I1   %  H%  F           N  ];   5  F              F           x P   |     
      t          
 
 F           ExteriorMap h77@ʸF                                        0     @       '              $          p    1                      $              d                            $          4                  $             p           T      `                H          	      	     	         
      
!    
     +   
    2    
         
                     0         <  #  L  "    3 \      2                       	     l                                                                        ,  +    8  -    D  /  T  .       `  2 	   l  4    3               *    ,                |        	           
             
 	        (                
 	                   F               F            $  
     31  X^x_!F                   "F           M   HZ  `Z  #F           r   2    $F  
         R terior powers o  %F           m 7       &F           n   >  a7'F           S   K      (F           T   W      )F           N       *F           i   ^  _  +F           j   Ȉ  Ј  ,F             )  -F            P                        
 
 .F  
         MatrixMinor     /F                                         0     @       '             $         p       |                                  3            !       (                                                                                  8       
     P             #       l      
         4           !         ! 	     d               0F                1F  
             2F           M sic;  \  3F           I1      4F           I2       5F  
         R   d  l  p      6F           i      (  7F           j   h  p  8F               9F            P                        
 
 :F  
         MatrixMinor rn I2.} ;F                                         0   !  @   !    '    !        ! $         p   "    |   "       "     "          "     "    3    "        "!       #(       #        #       #      #     #         #                   #              #       8       #
     P             ##       l      #
         4   #        "!         "! 	    " d               <F                =F  
              >F           M       ?F           I1  P  X  @F           I2      AF           R       BF           i   l  p  CF           j       DF            l0  C                       L                         C        xF              p     FF  
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         __sig__3 p  p  p  JF  
         __sig__4 G  G  G  KF  
         __sig__5 [  \   \  LF  
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         __sig__7  2) : i in NF  
         __sig__8       OF  
         __sig__9   <  @  PF  
      	   __sig__10   \  `  QF  
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      	   __sig__14 n D ];   UF        	   __sig__15             VF  
      	   __sig__16       WF  
      	   __sig__17       XF  
      	   __sig__18       YF  
      	   __sig__19 lse;  h  ZF  
      	   __sig__20   F  F  [F  
      	   __sig__21   XE  pE  \F  
      	   __sig__22   dM  |M  ]F  
      	   __sig__23   L  P  ^F  
      	   __sig__24 j] : j in _F  
      	   __sig__25 j] : j in F                       L                         F        a      F                F        F                       L                          F              F        F        F        B                       L               h P         B                       L                D         B                       L                 
         gF        8          C hF                  7  iF                     jF        t         (7  kF                 ^  lF                   mF                 X   nF                 r oF                 7  pF        8            qF        X         8  rF                   sF                   tF                 X   uF        p          vF                 8  wF                    E  n      h    X         X          X        $ X        ( X        , X        0 X        4 X        8 X        < X        @ X        D X        H X        L X        P X        T X        X X        \ X        ` X        d X        h X        l X        p X        t X        x X        | X            F        #      F        F                       L                         F        -      F        F                       L                         F              F        F                       L                         F              F        F                       L                          G              F        F                       L                          G              G        G                       L                         G              G        G                       L                         	G        +      G        G                       L               $           G        /      G        G              G        F                       L                         F                       L                         F        A      F        F                       L               ( $         F        C      F        F                       L               4 0         G        	      G        G                       L               T P         G        _      G        G                       L               ` \         G        =      G        G        F                       L               L H         F        F                       L               X T         F              F        F                       L               d `         F        ?      F        F                       L               p l         F        G      F        F                       L               | x         F              F        F                       L                         F              F        F                       L                         F        w      F        F                       L                         F        9      F        F                       L                         F        Q      F        F                       L                         F              F        F                       L                         <G              ;G        :G                       L                         ?G              >G        =G                       L                         BG        5      AG        @G                       L                         EG        A      DG        CG                       L                         HG        k      GG        FG                       L                          KG        C      JG        IG                       L               , (         NG        e      MG        LG                       L               8 4         QG              PG        OG                       L               D @         TG              SG        RG                       L               P L         WG        E      VG        UG                       L               \ X         ZG              YG        XG                       L               h d         ]G        3      \G        [G                       L               t p         `G              _G        ^G                       L                |         cG              bG        aG                       L                         fG        q      eG        dG                       L                         iG        ?      hG        gG                       L                         lG        C      kG                
G                       L               0 ,         G                       L               < 8         G        )      G        G                       L               H D         {G              zG        yG                       L                         ~G        U      }G        |G                       L                         G        -      G        G                       L                          G              G        G        /            G                       L               l h         G              G                       L               x t         !G        7       G        G                       L                         $G        {      #G        "G                       L                         'G        #      &G        %G                       L                         *G        I      )G        (G                       L                         -G     J         ,G        +G                       L                         0G        K      /G        .G                       L                         3G        '      2G        1G                       L                         6G              5G        4G                       L                         9G              8G        7G                       L                         G              G        G                       L               X T         G        #      G        G                       L               d `         G     %         G        G                       L               p l         G        )      G        G                       L               | x         G        ]      G        G                       L                         G              G        G                       L                         G              G        G                       L                         G              G        G                       L                         G        i      G        G                       L                         G        E      G        G                       L                         G        3      G        G                       L                         G              G        G                       L                         G              G        G                       L                         G              G        G                       L                         G        G      G        G                       L                          G        +      G        G                       L                         G        -      G        G                       L                         G        /      G        G                       L               $           G              G        G                       L               0 ,         G        ;      G        G                       L               < 8         G        m      G        G                       L               H D         G        )      G        G                       L               T P         G        W      G        G                       L               ` \         G        	      G        G                       L               l h         G        E      G        G                       L               x t         G              G        G                       L                         G        [      G        G                       L                         G        1      jG                       L                         oG              nG        mG                       L                         rG              qG        pG                       L                         uG        G      tG        sG                       L                         xG              wG        vG                       L                         C  4   0P   0  d   7`   4  d      $    ,                  $                    6	                            $                            ,                            B        %          G                       L                         G        G                       L                         G        u      G        G                       L               ( $         G              G        G                       L               4 0         G        S      G        G                       L               @ <         G              G        G                       L               L H         H    $˸L         
                  x              (                                                                                       d              <                                                 ,  +           @        T         '   h        d D   |          
                                                   ( ?     	                       7           0       	 D            X            l                                  Hi                                D ,                     i                          i  4          K   H  i      `    \            p               )         8j                             {     j         T       j        *                       $         C   8  j       5   L           8 `             t  e       $k     X     @k                 	      S     lk          T              0        k                        (       0 U   <  k          H P      	 d         l   x       0l            -                                                                  3           y   ,  l       @      l      T             h       m  |      m          H W                p              [       |m     m             	          m     m      m  0           D  1          	 X        n  l              	 8n                               pn              n  H    $˸                          
 d         :          l7    @      B P         G          : x   P      l>          ? <   p      G <   0      =          G (       xo         o                o         0     o  @      o  P     o  `      p                              8p       Dp               c         R               p       $                0      L   @           P          `      2   p                           L B        6               @       <        @               l                                        #   0     N       @          P      R   `     T       p        l       \        ^                       b        c                       g        h              b w                0     r  @     r   P     r  `      p     s              	               	      Xs       ds                                       s  0     s   @     s  P      `        p           t       	 ,t                                                                        0     o             H    ˸             H           $  @      (u  P       `         p             lu        	 |u        !                               	                                v   0     v  @      P        `      p     \v       $ hv       tv                              %        v       v                           0       @       (w  P     8w  `      p     Xw        dw               w             w       ( w       w                                ) 0       x  @     (x  P        `      $   p     H   w                  O                            ` Y        h                     2                     ,       L B   0     =     @          P      g   `     A       p              <        F            l       P                             `        /                      f         #       0          @     $ T   P     l     `         t p      r        t                       w        x                       }        ~                4       @                          | 0                       I            D 3                        $     c        8      d     0   0     e                   G        G                       L                         G        y      G        G                       L                         G        ;      G        G                       L                         G        s      G        G                       L                         G        7      G        G                       L                         G              G        G                       L                         G        1      G        G                       L                         G        ;      G        G                       L                         G        I      G        G                       L                         H        1      H         H                       L                           H        I      H        H                       L                           H              H        H                       L                            H               
H        	H                       L               ,  (          DH        $      CH        GH        %      FH        -H                       L                           JH        &      IH        HH                       L               (! $!         MH        (      LH        KH                       L               4! 0!         PH        *      OH                2H              H                       L               D  @          H                       L               P  L          H              H        H                       L               \  X          H              H        H                       L               h  d          H        
      H        H                       L               t  p           H              H        H                       L                 |          #H              "H        !H                       L                           &H              %H        $H                       L                           )H              (H        'H                       L                           ,H              +H        *H                       L                           bH        6      aH        `H                       L               ! !                 BH                       L               ! !         EH                       L               ! !         0H                       L                           5H              3H                       L                           8H              7H        6H                       L                           ;H              :H        9H                       L                           >H               =H        <H                       L                  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ww       5`5    cH                       L               ! !         fH                       L               ! !         kH        <      iH                       L               ! !         nH        >      mH        lH                       L               ! !         qH        @      pH        oH                       L               ! !         tH        B      sH        rH                       L               ! !         H        f      H        H                       L               " "         H        h      H        H                       L               " "         H        j      H        H                       L               " "         H        l      H        H                       L               " "         H        n      H        H                       L               " "         H        o      H        H        p      ~H                       L                " !         H                       L               " "         H        N      H        H                       L               " "         H        P      H        H                       L               $"  "         H        R      H        H                       L               0" ,"         H              H        H                       L               P# L#         H              H        H                       L               \# X#         H              H        H        H                       L               H" D"         H        H                       L               T" P"         H        Z      H        H                       L               `" \"         H        \      H        H                       L               l" h"         H        ^      H        H                       L               x" t"         H        `      H        H                       L               " "         H        b      H        H                       L               " "         H        d      H        H                       L               " "         (  >   n n tn n n n n \n n n xn n n to o ,p xp L @3 L 2 L K K 1 K tK K |K @K PK lK K K K J 1 0 0K J J J J J J J J 0 J 0 J J J |J / pJ hJ dJ @H                       L               " "         H        H                       L               " "         H        r      H        H                       L               " "         H        t      H        H                       L               # #         H        v      H        H                       L               # #         H        x      H        H                       L                # #         H        z      H        H                       L               ,# (#         H        |      H        H                       L               8# 4#         H        ~      H        H                       L               D# @#         H                       I  
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 
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                         ,
                                         #                                                                                         B  4   X(    $ d   8>0   # d      $    o#                  $                    6	                            $                            
                            3]     2   t           t t $               t     u u                   $                           4]              {                                                                                            `  
                     B  Z     	      k   !   Q     w   3   )         9     %   G   a   5   1     /         o   ?   E           i     #       -       )  7        I   S      ;   u        g              Y     +                    '         W           s     A   Q  C             =     c     m         e            y     K             ]         }     [          +    U                       O                 _     M         q     {                       
                                              (   *   ,     .       "   $   &   8   :   <   >   0   2   4   6   H   J   L   N   @   B   D   F   X   Z   \   ^   P   R   T   V   h   j   l   n   `   b   d   f     x   z   |   ~   p   r   t   v                                 *  ,      D˸    h /   O    1        2              T              , *             J   -       X C           5       0 &              ,       H             p        x 	          t 0                     
        !            H    (   /   -           The characters must be equal.  T -        $  ! ng-        -                                  T                    -           X   t -           Y     -     ,  0  4  8  <  @  D  H  L  P  T  -           M1  6   -           M2  x8 8 -           x  X: 8 -           ell = Weight-           sym   -           P rn M2!0;  -           X   t -           Y     -           Q  ,  -           i    -           --temp-- g                -            4  -           d  L           h        `  p          H    -  
         WindingElement 	pY	-                                         0   A   <   A     A     	    A $                   -     l  -           M    -            T*  -           |  L                   x            H    -           WindingSubmodule ]	,	ʸ}.} t -                                         0   F   <   F     F     	    F $                   -       -           M  ď ȏ -            D8  -                     Է                    H    -  
         WindingElement 	b	-                                        0   K
   <   K  L   K          K `         x   K        K    l   K       K      K     K    :    K         K              K $          L      L      L     L      L     4  L
           L          T  L   `  L     L        L H          L     L     L        L          L      L  p  L                   M     M
     M	      $  M          <  N     H  N#    T  N%  d  N$       |  N'       N*   p  N,      N+     N.    N-         N0    N/       N(       N&        N3     N"          Z    N     	    N 0                  -        3                            3                -         F ng-        -                                  T                    -           X     -           Y    -     ķ  з  k   -        -                                  (                    -            t  -        -                                  <                    -            Ht  -        -                                  <        ȷ  ̷          -     ط  ܷ        -           M  |  -                (                                                 p     $          T       `    
      	           H                     
      	                                                                 	             ,       8                T                                  H      `            	      |                                               D            (       4               X           l              	             	                                                                                          4       @    	 P          \    
                (              l                                                            4                   $                          T       `      l       x                          H  	                  
         	                                   
      T            8   	    D         
          ,       t                      	                       h                                  ,                                t                  T       `      l   	    x   
      	         	 	                                                                                $      4                `      	                  T  
          H  @                                       	                                            0        <  "           X  	     d      p  	    |   	            
            L                         	                 	   8	     D	               ,	          	     P	     \	      h	     t	      	    
   	  "  	  !      	        	           	      	                            )           t             x        p            H    )                                        0   +	   <   +     +        X   +$      +#      x   +8         +/      +;      +/               +/     + L   h        +             + $            ,,       ,/     ,1  (  ,0         ,+             P  ,     ,      ,               ,   D  ,   \  ,    x  ,      ,         ,
                  ,&           D  ,
 0             -,        -/   ,  -1  <  -0         -+             d  -:     p  -<    -9        -B     -?        -      -       -               -     -     -      -      -         -
 X               -&          `  -
 0      ,     ,7        |  .-     .,         /     /    /          /          /"       /'    /$        /               /)   \     $  /1    0  /3  @  /0      L  /9  \  /6      p  /)               0          0       0!    0        0'    0$         0              .    (  .   @  .               .     .     .      .      .         .   4             .    p  P       .7       .:     .<    .;         .6              .1      l      . 0            -G     	    ,               )  
   |                )           N ////////// )           R numerateP1!)           c  ! ` ")           d  " <* #)           d    $)           c           %)                &)             L                            H    ')  
         ManinSymbolList ////()  h                                      <   F    $   F      F         F
 0          l   G   x   G     G          G     G        G      t  G
 `            I        I      J       J     K      K     K!  ,  K      8  L    D  L   P  M    \  M   h  H      H
 	    H                    ))        3                   c         d         e      *)               +)           k pXʸ,)           N eturn u -)           F  ԓ d .)           p1list  m /)           n   P 0)                1)           ̤  H   Ф     Ԥ        Ȥ            H    2)           UnwindManinSymbol     ˸3)                                        <   g    $   g       g   x   g
 0         h   h	     h         h \             i       i 
    i        i             j       j     j
          k      k
         P  j              4  m	    @  m     m        m (       p  n     n        n       n      n    n         n    n        n         n   $  n d          o
      o       o 	    o                    4)  
      d                     5)  
   ؤ  ܤ            6)           i  Py     7)           mlist  t 8)           p1list rt.  9)           n   \ :)           ind ԗ `r ;)           uv  x ` <)           w  Py | =)                >)                                          H    ?)  
         WindManinSymbol ener@)  .                                       <   v
    H   v    0   v    T   v  d   v     t   v          v 	    v     	    v $               A)        d      B)           C)           w eturn i D)           ind 3  E)           mlist  8 F)                G)           $  H   (     <                     H    H)           ManinSymbolApply ʸst)  ʸI)                                       <   }    $   }       }      } 0         h   ~#       ~%    \   ~      ~"         ~     t       ~           ~          ~
                             $  
         $      0    @        L       X     d    t                 #    "                 &     (    '         +     .    -       *    	   %        (  2   4  4  D  3       P  7   \  :  l  9     |  6          =     ?    >         B     E    D       A    	   <                                   l  
   	   	   D      \  #   8                     P         
    0         
                                                             	                        T     `              |              	                       
     '                               	    	     $   
   0     L                            	    	         p    h       H  x                                          X                                        L          ,       @              
                                             	                             $    4         @    P          \  !   h  #  x  "    	             (     *    )         ,    +       &              |   t                            8      D      P               	     ,                 `            !                            
      H
            	  -    	  1  	  0      (	  5  8	  4         ,             `	      l	     x	   	 	       	         	      	    	      
   	   	 	                          
     T	             '      	       
       
       ,
               t
     
    
         
  "                     
 h
  
                 \
  
       
       
  	     
              J)        3          d                             4      L)        M)                                  T        ,  0          N)           x  )  O)     @  D  H  L  P  T  X  \  `  d  h  l  p  t  x  |              P)           g eturn  Q)           i           R)           mlist   S)           eps u | T)  
         k qEnum Elt,       U)           uv st`k; th V)           w  i j W)           ind ,  X)           p1list   Y)           uvg  mlist`pZ)           act_uv ];  [)           scalar  } \)           R rn t n ])           x  )  ^)           hP   f _)           pol L7 Dz `)           n        a)           w  ,  b)           ans 1list; ec)           x  t } d)                e)             `                  ԥ          H    f)           ModularSymbolApply          g)                                        <   	    $       T   
   0             h   H                    "                                           #                     "     $  $  #       0  '   <  ) # L  (     \  &     l  !       x  -     /    .       ,         2     4 #   3       1         6     8    7         ;     = # ,  <     <  :    	 L  5           0           t                           |  	      
                                     $          ,          @                      `     l     x          $                 T                   	                                     $     0    @         L    \      	 l         x                                 !     #    "         &    %    	             
              ,     8    H         T    d         p     |          	             	                                           !     #  $  "    	   0  &  @  %    	 P         l  
                	                  
         
           
          	                   h)  
               c          i)                   ĥ  ȥ  ̥  Х  j)           M sic; x in k)           g           l)           s  i  m)           R /d.}  a pan)           h `mlist`R; o)           hP  -g[3]*R.p)           a (s[1]);  Rq)           b  5  r)           c  Pe $ s)           d  З | t)  
         gx plode(s[2][2]);  u)                v)                                ܥ            H    w)           ModularSymbolApply ʸrn ]];  x)  8                                         2     <       H   !    T   # %             
     0              *    $   d        
          	                        y)                 z)           M  7 z {)           g   4 |)           s           })           term o l ~)                )             X                   p          H    )  
         Sparse2Quotient  ˸)                                      0       <                        $        x                                                            l                                        (       4  #                                 P                   \              x                                                     	                     
      L   	   X     d    t            
                                   d  	 @           	                         
   (     4    D       T                  	                 
 x          	                                                                      ,      8    H             \       h      t                              
                                                               ,  T     8      D    T                       t   
                                h           
                               
        (     8       H                 d      p   	                           
                                          	 X              
   $     0    @                           p   
   |                               d                                                 8                 D         ,     \      h                                        x           	  
                                 	           	                   T	        (	           	          H	     x	            D
    l	    	       	       	              4	        	            	      	   
   
  "   
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              
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         &             P       h      t   
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       &    	       &                P                                         (  	    4              P      \                          l                           	    	             	     	                D  x         8                 \         ,          |       P                    p                    	     ,                                        	         0         <                 x       L                    l          X       `                '             #    (     %                                              0      ,       D                                           	                                 (                                L      X      d  $  t  #                    @                                         t         !
      !       ! 	    !               )        l      c          c          c              )                $  (  ,  0  4  8  <  @  D  H  L  P  T  X  \  `  d  h  l      )           rels ; larSy)           relc    )           n   H )           F  8x 7 )           free  0 )           i  L x )           coef   )           i  |l q )  
         related_to_me  Tm )           i  + l )           t    )           c1 rels[i]; )           c2  x+ o )           die c1*x_fre)           x    )           i oef[x] := )  
         --temp--            )  
         --temp--            )  
         --temp--            )           i  dg } )           i _2}  <----)           x  ,j : )  
         ykey        -1; en  )           i    )                )           |  0                x            H    )  
         Pivots   or lt Tr )  `                                         6   0  6
 $             7      8      8 P         |   9       9     9          9     9         :	      :     :                  9 p          <       <     <        &       T  7    D   \         >
 	    > H                  )        l      )                 )           B x  )  
         pivots basis. ****/ )           b    )           j   L )                )             \                  Ħ          H    )  
         Quotient ; s, j);  )  X                                      0   C   @   C       L   C&     C#         C $         |   D (    D
          D     D         E      E         8  D p                 G       G    (  G     G#       G%      G
      G    	    G               )     %                        d      )                 )           ring        )           rels l Xl )           n  p t )           K  (m ,t )        
   ringchoice els, n, K)  X )                )           Ц  |   Ԧ             ̦  `      d  H    )  
      	   Quotient2  \   )                                          J(       K   H   L     T   L     L         L <              K 0   d             N       O	      P	      P	               O                 R       R      R        R         0  S    <  S       S             d  S    p  S #    S         S     X             S    $         S 0          (  S             T0       T&      T     T  $  T       0  T    <  T   H  T  X  T    # h  T        T         T                  T!      x      T         )    T         T                  T+             T           X  T   	   	   H  U *    U        U <  	      x  V     V 	     V     V               V   (  V l  
       W      W      W          	      X      X3 + (  X2       4  X9    @  X; # P  X:        X6          X      W'   `             X       l      W'  8               W#          W      W                W             W 0          t  W         H  Y    T  Y  d  Y    ,    Y        Y <         ]0      ]3      ]/              ]       ]      ]! 
     ]"      ]$ #   ]#        ]!      $  ]! -    ]       @  [ . P  [       \  \	    h  \    t  \      \"      \7 .   \6       \#       \       \    #   \
        [         Z     4             ]          H  Z              Z )    Z         Z     <             ]*      X       Z       t       Z            _	      `	      `	            ,  _              b      b ,    b      	  b             c0       c&    d  c   p  c    c         c      c     c    c    #   c        c         c     X             c!    L      $	  c         )    c         c     	             c+    @  4	       c       P	    ,
  c h	  	     	  d     	  d! 	   	  d%  	  d$       	  d+ / 	  d       	  d. 	    
  d0   
  d.      
  d. 0    d      x
  d 	        L
  e    X
  e 1 h
  e        e      
  e @
        
  f 2    f      
  f 
        
  g    
  g ,    g        g 
  
       h      h      h            8  h 
   D  h   P  h    \  h   l  h         h      h     ,             h    
  x       h             h           j     j      j        j        $  l    0  l      l             X  l#    d  l+ 3    l%          l      l L  t             l             l 0          @  l          m      m     m        n 
   $  n     n       n/    H  n     T  n"    `  n%     n!         n     <             n*    0  p      n             n        n     n     (  n            n      n     n        n             m          d  p    p  p     p    
     q      q #    q       q            q      q     q        q             p    X      D  N            8  t
       t 	    t ,                  )                  ئ         ܦ                                                               )  
         # relations =   z )  
         ring reduction  ` )           vector space reduction   )  "                                   $  (  ,  0  4  8  <  @  D  H  L  P  T  X  \      )           rels rn { )           n   [ )           K  $  )           ring  { )           R  <   )           i  p% % )           vars " " )           r  u  )           t  ,m l )           Rels  {@ R.i)           W  ) `{ )           i  З | )           g sts   )  
         gens  quo<R|Rels>;  )           Z .i } @};  )           i  " <* )           t    	@ 	)           quot   )           V  	 	ʸ)           r  <e 7 )           t  xy $v )           S  ! Ĭ )           m  d  )           B );   )           i  , + )           pivots      )           i  5 g )           i   ̙ )           j  \ 0 )           i s];   )                )              $   d  )           p  H   t             l            H    )           ManSym2termQuotient  	ʸ)        e                                                          l         l          )                ent )        )                                  <        x  |          )                    )        )                                  <                    )                             ħ  ȧ  ̧  Ч  ԧ  ا  ܧ      )           mlist n T )           eps     )           sign  <" )           n sign) ////)           K  D% % )           S mlist`F; m)           I  +   )           i  `     )  
         xS -1,0,  0,1]; ̗ )           i  c L )           S_rels inSym)           i  X4 (o )           S_relc   )           i      )           xI    )           i  * , )           I_rels  % )           i       )           I_relc  { )  
         rels c := []; !1, -s)           relc f e )                )             H     	             d          H    )           ManSym3termQuotient   	ʸc,n,K); )        e                  3                                       l                          )            T   *        *                                  <                     *                *        *                                  <                    *            $  (  ,  0  4  8  <  @  D  H  L  P  T  X  \  `  *     x  *  
         mlist n [i] gt 0];  *           eps & ! (     Print(M148); Symbols*           Skey  0 *                ;*       	*           Squot  ؃ 
*           Scoef  j *  
         N eturn if  + + [  
   D148:=Decomposition(M148); z*       *           n ations. uo*           F  k k *           k    { *           T ist`k; he *           TT  h ̖ *           i  L" ! *       *           mask     *                *     $  )  R                                      <   }
    $   }       }      } 0          t   ~
   \   ~       ~      ~ h           
                  
                 4       7      3                           ,  !    8  ' 4                               .       H              d       |         .      1      -               6 	     9    8       5       $  ?     <    	   @      L   	   X     d     p  "                                4             ( 	                            
       .      1      -             @  6    L  9  \  8     l  5       x  ?     <                                                           "                              4               (       0              L    @   d                             7      :      6                      "       $       * 4                               1      0              L       d         2      5      1                                "     &                                               ,      0              L       d         7      :      6                                                    0         <  !    H  $   T  '   `  +  p  #                                                  1                                         ,                                      
   d      p   5             X                 5          	                   !      &    	  (                 	      	                  )                                        <       $                 0          t      \                 h                                                                 
      	           $             @      L                                   h              
   4  t                                                                       8      D    T                 p  #    |  %       '      - 4   "        2     1      0   d     	     #      &       (      . 4   "         3     2      P                      D     p     |                     d                                      P                         (  #  8  "       D  &    P  ,  `  +      |                                                                         !      '     )  ,  (     <  &      X               d     p                                                     #      )     ,    +       (      4                                       &           	 ,            
      l                                                                      <                              d  )    p  +     |  -      3 4    (                                                                  "    ,  (   8  *  H  )     X  '                                              X  t    
           	     )      ,       .      4 4    (       	     	    ,	         8	      D	     P	    `	       p	       	         	  "    	  (   	  *  	  )     	  '                             	                   	    0
         	    L
             6                                     \
              x
        
       (       
     
      
                     
  
           	                   *           rels ' 8' *           j  4 ' *           t  d c *           tt  ,_ x_ *           i     *           x      [<x[1*           x  \ \ *           p  h           t        l  |          H    *           ModularSymbols 	xH	 	ʸ*  $                                       0   , 7 @   +      L   /    X   1 8         	     $                *             h                               H    !*  
         ModularSymbols  p4 "*  $                                       0   , 7 @   +       L   /    X   1 8         	     $               #*             $*           N sic; arSym%*           k  T, ` &*                '*                                            H    (*  
         ModularSymbols  " )*  Z                                      0      <     L              `   |      l    9 |                                                  " 8         	          <   $                , 7   +          /    ,  1 8         	                        **           +*           N sic; arSym,*           k  H % -*           sign ularSym.*                /*           Ĩ  @           Ȩ          ܨ          H    0*  
         ModularSymbols  h 1*  2                                      0    9              $       \   ,    h   . 7 x   +          1       3 8         	     P               2*     ̨  Ш  Ԩ  ب      3*           N sic; arSym4*  
         k         5*           sign    j   6*           p     7*                8*             X                               H    9*  
         ModularSymbols  l :*                                          0      <       H    8         	     $               <*           eps c; arSym=*                >*              X                               H    ?*           ModularSymbols 	xQ	@	ʸ@*                                          0       <       H    8         	     $               A*             B*           eps P  C*           k  Tz { D*                E*                      \                    H    F*           ModularSymbols 	W	@	ʸG*                                     0       <    : L              `         l      x   " :                                                       4   $                                                      h                X   ;             L            <             |             =             	                             $    #       (  *  `  '       t  3    P  ;  t  :     t  , 8  D       ,           8          	                         	                                	                               \  	     		         
      
	 l       	 P  x        h                                                          $       0      H  !                	     <         X            =                                          ,                                                	               X   = h                  L              @  t            =                                          P                .     (  5    @  :           -      d       4   x            
    	          
               =       	                                       "     "      ,  "     "       H  #     T  #    l  #!   <  #      #     	    # `      "   |           & =     '        '      
     '      '            h  &              )'     (  ).    4  )3 	   @  ): 
   X  )A     )      )&      |  )     L     )          )
            *      + =   +         +      +            	  *            	  -  $	  -      0	  -     -       L	  .     X	  .    p	  .!   @	  .      .     	    . d	    	  - 	  	         	  1    	  1  	  1    ,    1       
  1 	         
  <# 2 
  <"    >    <      X
  < 	        @
  =      =   4
  =  |
  =     L
           >  
  >
     p
       >  
  >       
        ?  
  ?
     
       ?    ?       
         @  $  @
     
       @  H  @               A  h  A
     <       A    A       \        B    B
            B    B               C    C
            C    C             E       E   ,  F 	   8  F   D  G 
   P  G   \  H    h  H   t  I      I     D      D    D
            D    D              M     M!       M      M&       M%     M    $  M   0  M    <  M   L  M         M      M                  M      X       M       t     M           M	      M	  D  M	               N     O      O =    O         O      O            h  N   ,            Q
 	    Q \              H*  `      $         (         ,         0         4         8         <         @         D         H         L         P         3                                                        f         g         h         i         j                           j                             j         T         X      I*           sign must be -1, 0, or 1 ] ] l] J*        3   Modular symbols are only defined for weight k >= 2. P \ K*        #   Creating M_%o(Gamma_1(%o),eps;F_%o) @  L*           ^+  T0 3 M*           ^-  ) } N*           
  \k dk O*           Step I.   Manin symbols list.  @ P*  
      	    seconds.  t) ) Q*           Step II.  2-term relations. c c R*  
      	    seconds.  (\ [ S*           Step III. 3-term relations.   T*  
      	    seconds.  $h x U*  
         ,  Verbose then : v V*  
         seconds.    W*     `  d  h  l  p  t  x  |                      X*           eps & Ę Y*           k    Z*           sign ularSym[*           N  `  \*           F    ]*           tt  4     ^*           t eSuperverb_*           mlist  <" `*           Sgens  db a*           Squot   b b*           Scoef  ta c*           Tgens   d*  
         Tquot    D     e*           V  e  5 f*           M n the futug*           v  P H h*                i*             @                  ԩ          H    j*  
         TrivialSpace   k*                                        0   U <    U      |   U $         `   V    l   V ,    V         V T            W ;    W         W             X# 2    X"    >    X        X              Y
  ,  Y              Y  P  Y                Z
  p  Z     D       Z    Z       d        [    [	            [    [               \    \
            \    \               ]
  <  ]            ]    ]       0    `  ^   l  ^$   x  ^(     ^/ 	    _ 
    _     _     _#     _'     _.      ^      ^    ^
     T       ^  @  ^            (  `      `     `  d  `     4           a
 	    a X                  l*  4      3                                               f         l         g         l         h         l         i         l         j         l                   m*  
         ĩ  ȩ  ̩  Щ  n*           k    o*           eps (     p*           sign       q*           F   		r*           V         s*           N  t  i t*           M aracterLevu*                v*                             ܩ            H    w*           Weight   x*  >                                       <   f    $   f    H   f     f        d   f7 ? t   f6    @    f)     	    f X        f 0                 g
      g       g 	    g                y*  
      3          3           {*           M  &  ' |*                }*             H                             H    ~*           Level  ned M*                                         <   l
    $   l       l 	    l 0               *               *           M  \ \\ *                *             H                   (          H    *  
      	   Conductor    *                                         <   q
    $   q       q 	    q 0               *               *           M sic; el of*                *           4     8     <        0  D          H    *  
      	   BaseField   4 *  >                                       <   v    $   v    H   v     v        d   w$ ? t   w#    A    w     	    w X        v 0                 y
      y       y 	    y                *  
                         *     @  *           M sic; el of*                *           P  L   T     \        L  h          H    *  
      	   Character ie		*                                         <   ~    $   ~      ~     `   ~     0      ~             ~                     ~       ~     ~                         	    	         ~                 ,  ~      ~    ~        `     H      x     T          	    	 l       ~      ~    ~              	                   8         t                          *     c                   c             5               c             X      *            Character -- invalid input type. h d  *     `  d      *           M     *           --temp--                   *                *           t     x     |        p            H    *  
         IsPlusQuotient ; rac*  P                                       <       $       H                p   &   X   (       '   d   *       )      2     /     	     |        0                 
                            	                    *                 5                            *       *           M    *                *                                         H    *  
         IsMinusQuotient n th*  P                                       <       $       H                p   &   X   (       '   d   *       )     2     /     	     |        0                 
                           	                    *                 5                            *       *           M  (b b *                *                                         H    *  
         Sign ; n eq -1; n th*  B                                       <       $       H                p   &   X   (       '   d   *       ) 	     |         0                 
              	                    *                 5                            *       *           M   $ *                *           Ȫ  t   ̪     Ъ        Ī  ت          H    *  
         IsogenyClass      *  6                                       <       $       H                   	     X         0   d              
              	                    *  
      I         I          *     Ԫ  *           A sic; n;  M*                *             0          	                  H    *  
         HeilbronnMerel  7 *                                             P    $                  D        p        |                                                                                            l            @      L                        4  \                                                                                      ,      8                              &                T         p                               ! B                                           0       <  "    H  %  X  $    C h  !       t  +    (                                  $      '    &    C   #         *       ,                            &                              8     t                                                                                                               &                8        h  T              P  l      
                 d           
 	                   *        l      *                        *           n sic; ; s *           H SeqEnum ***           i  L x *           a  8k k *           d  u p *           bc  ad-bc=n *           b  D ! *           c  dc Dc *           c  x H *                *              @   $     x                    H    *           HeilbronnCremona   < *                                        0    9              $       \      h                   	     x        P                                                       
             l             4    D        P    `      D p          |  "     $    #    C   !                          
                                              @                 p   4         `  '     &        $ T           -     +            3     1   	         :     8   
         A     ?            G   |  E        0      <      H      T      `                    X       $  &                                             E          P                 $      0    @                     	      p                d     	                                                         
            8        
            ,        X  #    d  %  t  $         (     '          L           2     /            <   <  9                                   "                            &                       (          
 	                   *  
      8         t          *                       <            *  
       (     <            *     D  P  \  h      *        *                                  (        0  4          *                       *        *                                  <        <  @          *                       *        *                                  <        H  L          *                      *        *                                  <        T  X          *                      *        *                                  <        `  d          *                *        *                                  <        l  p          *     |                          *           p sic; if  *           ans y  *  
         r [[1,0, 0,p]];  *           x1  $  *           x2   T+ *           y1  ̯ z *           y2    *           a  d  *           b    @ *           c  ! Ē *           x3  $ # *           y3  H% T% *           q   $( *                *             0                     ȫ          H    *  
      	   Heilbronn   X *  <                                                      $       T    9            p    F         	     d           G         	              H                         *     ī  *           n sic;   *                *           ԫ  `   ث  
   ܫ        Ы            H    *            InitialManinSymbolGenListToSquot    *  &                                     <       $       T      0                	 H                                         t                                         L  	          (           @                   	 4        x     `           l              	            H                    ,          X                $     0  	    <  
   L  	         	   H     	           	              
                                               x   ,                   d              ,    
   8      D     T                        	             	             |        
                            
      $      &     %        #                               l   
   l    	      
 	     `                  *  "               j                  f                  h                  g                 c              *                                  *           m  Hh  *           M  ؆  *  
         Tmat TupFld,    ,˸*           Tquot  dk *           V  5 \e *           Sgens  z *           Scoef   *           Squot  (  +  
         W = M`quot`Squot;  +           v  , + +           t  d  d +  
         --temp--        r+	+                +             `         $          D          H    +           InitialManinSymbolGenListToM n ]];  +                                        <       $       T      0                	 H            	   t   	       	      	       	      		             
      
     
        
      L  
          (           @                   	 4            ,    x                                                                               (       8       H                        l             '    `  X            t        )    
     	                       +                 h                  j                  g          	+  
   (  ,  0  4  8  <  @  
+           m    +           M  d  +           Scoef    +           Tquot    +           V    +           Squot   +           t  |2  +                +           P  L           T        L  `          H    +           Tn ic;   *Tq+                                         0       <    I         	     $                   +     X  \      +           M n m];  +           n  t s +                +           l  0           p        h  |          H    +           HeckeOperator 	h	Z	ʸ+  *                                                     $       T       `   $ J p   #    I         	     H               +     t  x      +           M  w ! +           n  0 H +                 +                                         H    !+  
         HeckeOperator 		"+                                        0   ! 1 @   !       L   !     !       h   "     t   "        " K    "         "       "      "         " 	    " \       ! $                %      %       %   H  %	           <  &   $  &       &     &	 0         t  '   \  '       '     '	 h           )     )       )     )	           *     *       *   (  *	           +     +       +   `  +	         T  ,   <  ,       ,     ,	 H          -   t  -       -     -	   	        0       0# 1   0"    L    0      0  0   
   	     1     1     1        1      P  1      	     2     2 D        p  4    |  4    4    ,    4        4 d     
    5      5      5% 1   5$         53 1    52    /   5        57   (  6"    4  6&  D  6%         6!          	   l  6    x  6     6         6     `             6            6             57         57     5          8       8  0  8         8             X  9    d  9    p  9    9        9      x  9 L           <      ;*      ;,      ;/      ;5 4    ;)         ;                  <          @  ;         6 P  ;        \  =    h  = M    :+        : $         >       >     >       &       l  8            @      @      @    @         @  (  @    / 8  @      D  @$    P  @&   `  @$         @$     @          A
 
     A
     A      A      A    A        A         A 	    A               #+  *                                                     f         g         i         j         l                                       $+                             Ĭ  Ȭ  ̬  Ь  Ԭ  ج  ܬ      %+           M   z &+           Heil  $ '+           F  @' ' (+           mlist  * )+           eps p. , *+           quot b b ++           Sgens  ` ,+           Squot  ] -+           Tgens  L[ .+           Tquot  < /+  
         Mn  quot`Tquot;  " 0+           V    1+           T    2+           W   ` 3+           i  P  4+           Tmat rSpace(5+           j (V)) !  6+           i  d0 42 7+           h  d P; 8+  
         v  Sgens[Tgens[j]]; 9+  
         S ;  ~T,v); at); h i:+                ;+             0                             H    <+  
         TnSparse mat		=+  B                                        G      G       $         H    `   I       I      I T               H H   l              K       K  J    K          K$ N    K     	    K                >+              ?+  
      	   TnSparse   hz 0{ @+           A+           M    B+           n  X4 (o C+  
      	   sparsevec   ~ 7 D+                E+                   
   $          p          H    F+  
         TnSparse e(M	(	G+                                        0   T 1 @   T       L   T     T       h   U     t   U      U       U      U         U 	    U \        T $                 W      W       W   ,  W	              X     X       X   d  X	          X  Y   @  Y       Y     Y	 L           Z   x  Z       Z     Z	            [     [       [     [	            \     \       \   D  \	         8  ]      ]       ]   |  ]	 ,  	      p  ^   X  ^       ^     ^	 d  
        `       `# 1   `"    L    `      (  `      	    a       a      a	      a
     a	         a	     a            b    T  c
 	   `  c    l  c   x  c    c       c        c      p  c H          d     d     d
          e:      e       e"      e%       e+ 4 0  e      <  e0     e/         e                  e5      L       e       h       e
            g;      g$      g&      g)      g/ 4    g#         g                  g6          L  g         6    g         g
 0         d     \      i      i     i    i         i-       i/ O   i,        i        i              4  b    <          k
 	    k (                  H+  "                          3                                     f         i         j                     I+     (  ,  0  4  8  <  @  D  H  L  P  T  X  \  `  d  h  l      J+           M    % K+           Heil & Ę L+  
      	   sparsevec   ) M+           F  ` ` N+           k  X^ T^ O+           mlist k;   P+           eps Y Y Q+           quot  x R+           Sgens  @ S+           Tgens   T+           Tquot  H U+  
         Mn  quot`Tquot; \ V+           v     W+           m  ؼ ̼ X+           i    l Y+           h   H Z+           x  x ̵ [+           h  ܚ  \+                ]+           |  0                x            H    ^+           SparseRepresentation p  q _+  v                                         	   `    $          P    P             D                                                   	            
                                       0         <                              &               X             t   t        
 	                   `+        l      a+           b+           v his by: GHc+           sp rse repred+           i  pi ` e+                f+             |                            H    g+        
   HeckeBound ,			ʸh+  p                                       <       $       T        `      H       l    Q          t   0                                                                        (                     X              L                  @                              
 	                   i+        3                                                         j+        D     Warning: William Stein has not proved that his bound on the number + + k+        D     of Hecke operators needed to generate the Hecke algebra is correct  . l+        #     when Character(M) is not trivial. D/ / m+             n+           M    o+  
         b s a Z-module.} hatp+                q+           ̭             Э        ȭ  ܭ          H    r+  
      
   HeckeBound  \ ] s+  0                                       <       H       0      X        h         t   !         D         	     $                   t+     ԭ  ح      u+           k xG0; haracv+           N  d[ [ w+                x+                                         H    y+           VectorSpaceZBasis 		ʸ;   z+                                         0      <      H   "  X        h           t   .      0     /    P    -        &    ,          ,   $      R                 $     #         1 1   0    /                      L  
    X  
   d       p                   h   @                                                        H  "              0  #   <  "     " >    !     	     $         X            S       2          x              +                  !      "     !         !                        &          h         4  >         	     L              {+                                      |+  
                    }+           B    ~+           V ld  H +           Mat ` x +           X ension(V))+           Latbase 48 +           v  d{  +                +             @                     8          H    +  
      	   HeckeSpan    +  t                                      0    T          p    $          `    Q          t   T            	   H                  +       .      *                                N                                %           d         0  5                         U         	                       +  
      $  (  ,  0  4      +           M sic; rSpac+           v  T pT +  
         s tion computes  +           b  k l +           n  x 5 +           B  li { +                +           D             H  
      @  t          H    +  
      	   HeckeSpan ac		+                                        0   . 2    -       L    T                  @              #    $   \               x                       Q                              !                   0   J                  $                    @              \       t           :     ,      /      +                                       $  ! N                               &      4              P            h             5                     6               	   	      U         	                       +     L  P  T  X  \  `  d  h  l  p      +           M  8= 8 +           V  i 2 +           v    +  
         S basis.} putes ,u +           b  D ` +           n  % % +           H   l +           s  ` ` +           n  c lc +           B eilbronn(n+                +           e   ,  0  +           VEinv     +             @          	                  H    +  
      
   FastTnData mat< V, e+                                        0   	               $          `      l       x                         2              T                 
                     4         $                               `       l     T      x               /           !     6      9      5               #      %      (      *     )        $         "                  0      0    p  C    |  F      B              =    d  L      "             !         !   $  	 H                           	        D      P     \      h  "   t  %      ,           
 	     8              +                            6         k         l      +                       +           M   @ +           V    +           n ata needed+           B   x +           e   Լ +           j   D2 +           i  D T +  
         VE ots(B);    ns.  +           VEinv 1..n],+                +           Į  \           Ȯ          Ԯ          H    +  
      
   FastTnData Dt	8u	+  "                                       0       <    2 L       V         	     $                   +     ̮  Ю      +           M  ( $ +           V     +                +             t                   ܮ            H    +           FastTn nData+  (                                       0       <       H       T   ( J d   '    W         	     $                   +           +           M 6789:;IJKL+  
         FastData  !"0123'(+           n  i  +                +              H                  @          H    +           FastTn n(M,F+                                        <       $                	 0         t      \                	 h                          	               1            	                            P  	          D     ,            |  	 8       p  0    |  3      /                                   	     "    !                                  N                               * 	   d  ,              H      	 `  
                          /           "      $     "         "     	        $      0      <      H   / X        d  " 
   p  $     "         "   P  	                       L                       . X   -       #       $  5  4  4      D            	                   +                 6         k         l                                       +                  $  (  ,  0  4  8  <  +           M ); p @s +  
         FastData } 0 H +           n  dg } +           H  k j +           F   ~ 7 +           V = M`F; f T+           m    +           e    +           VEinv  p" +           i   - +  
         TE  FastData`VEinv; +           Vmat b b +           TEmat  x] +                +           L  t           P        H  `          H    +           FastTn ixAlg+  (                                      0        <       H       T   ( J d   '    W         	     $                   +     T  X  \  +  
         FastData    +           n  T , +           M    +                +           l  L           p        h            H    +           FastTn n(M,F+  0                                       0       <    V              $          l       x           W         	     `                   +     t  x  |        +           M );  x +           V  t  +           n  8 , +  
         FastData 	p|	ʸ+                +             L                               H    +           FastTn n(M, +  2                                      0        <    V              $          l       x                 ! W         	     `               +               +           M  < ( +           V  | $| +           n  ~ ~ +           H    +  
         FastData  S T +                +             L                     د          H    +           FastTn n(M, +  P                                       0       <    V             $            .     x                        "       $     #    W             
     l              )    `           
          	                    +  
     į  ȯ  ̯  Я  ԯ      +           M  _ d_ +           V  ` ` +           nlist 	x	+           H um,  D^ +  
         FastData \ T4 9 +           n    +                +             L                                H    +           FastTn Tn(M,+  F                                       0   $    <   $ V    $         $ $            %(     x   %       %       % W    %         %
     l              %#    `           %
          	    %                +               +           M  n l +           V  \   +           nlist   +  
         FastData    +           n       ,                ,             @                  4          H    ,           ActionOnModularSymbolsBasis ********,                                        0   0 Y    0      8  0 $        `   20    l   24  |   23         2/                2        2        2"       2$     2#    %    2         2	                   2*    T           2	           $  2        X  41    d  45  t  44         40               4       4"      4%    4$    Z    4         4	                  4+    L         4	             4         P  5    \  5   D  5    h  5    t  5& 1   5%    L   5        5)      5*     5)         5) 	    5 8              ,  
                           ,  
          $  (  ,  0  ,           g  4 ' ,           M  ) ) ,           B  <) D) 	,           i  `a Ta 
,           gB ply g to ,           i  Y Y ,           gM  ] l] ,                ,           @     D     H  
      <  t          H    ,           Wq turn  ,                                        <   A    $   A   L   A      X   A     A        t   B0 ?    B/          B3 [    B"    X    B           B7 \    B     	    B h       A 0                D       D
       D	   P  D           D  E   ,  E
       E	     E 8        p  F
    |  F     F        F d       G
      G 
   G         G     G      4  G        H
     H 
   H       $  H     H      x  H       \  I   D  I    h  I     I        I P      K     K        K      K      K    K        K        K       K      K      \  K         0  L	   <  L     L    
    L        L $  L          M       M     M     t              N	     J          O      O 
   O         O     O        O      (  Q   4  Q   D  Q      P  Q    \  Q!    h  Q#  x  Q"        Q        Q    Q        Q        Q
          Q          Q        l  Q	            R	      R  ,  R
       8  R    D  R    P  R      R               R           S$       S'     S      S#        S            T     T      T     T      p  T   	   	     U    (  U  8  U         U   L     X  U 	   d  U 
 t  U         U    U         U             V      V     V     V        V      V     V    V        V      (  V   4  V   D  V        V        V       ]          U   T            X
 	    X                   ,                  3                                                                         ,     L  P  T  X  \  `  d  h  l  p      ,           M    ,           q   @ ,           N   | ,           k    ,  
         d IsTrivial(M`eps); ,           x  ` ` ,           y  a a ,           g := XGCD(q,,  
         A *x, y, N, q];     ,           p   { 4z ,                ,             X                |            H    ,           StarInvolution 			ʸ ,                                         0   _&     H   _2    $   _
      _%     	    _ <               !,              ",                    #,        $,                                  <                    %,       &,           M Ч		',                (,             \                               H    ),           Tnpoly nOnMo*,  "                                       0   f(    <   f* I L   f'    ^    f     	    f $                   +,             ,,           n 	PV	   -,           M 	4r	   .,                /,           İ  @   Ȱ     ̰                    H    0,  
         Restrict Cha	 	1,                                        0   n 2    n         n $          `   o   l   o   x   o     o        o          o. 1    o-    ,    o        o T           p       p% 1    p$         p             (  p	    4  p	   @  p
    L  p    X  p  h  p      x  p
         p
      p                  p              p             p            q       q \    q     	    q               2,                3,  
   а  ԰  ذ  ܰ          4,           A   p	д	5,           L   p		6,  
         Z is Basis(W).} to W7,           V sis(L);   8,           i       9,           B 	    :,                ;,             @                               H    <,  
         Restrict t (ȸ		=,  *                                      0   y 2    y      |   y $          `   z    l   z \    z     	    z T                   >,            ?,           A   @	 	@,           W        A,           B  '     B,                C,             @                     (          H    D,  
         Restrict t (A, B);  E,  *                                      0    2          |    $          `       l    \         	     T                   F,          $  G,           A      H,           W   I,           B           J,                K,           4  @   8     <        0  P          H    L,  
         Restrict t (A, B);  M,                                        0    _             $         `        l      x   !      #                        (     '    L            +      .       2    1         -             ,      8      D  ! # T           `  #  p  "    `                                (                      6           +         + 	     T                   N,                O,     @  D  H  L      P,           A         Q,           B         R,           S is B.} t 	S,           i  & ~ T,                U,           \  @           `        X  t          H    V,  
         KernelOn 5 X  W,                                        0   	               $         `       l                   	     |     X   T                  a                b                         D        ) a (  (       4  /  D  ,                              t   c             h          8 2   7         ; d   1    >         	                   X,     d  h  l  p      Y,           A sic; [CoorZ,           B  D{ L [,           n odTupFld  \,           K ) eq n;  ],                ^,             \                   |            H    _,  
         KernelOn b a a `,  "                                       0       <    2 L       e         	     $                   a,             b,           A sic; rSpacc,           W  _ ` d,                e,             h                               H    f,           HeckeOperatorOn k		ʸg,  $                                       0        <   " I L          X   & \         	     $               h,           i,           M  t h j,           V    k,           n   P l,                m,             x                     ̱          H    n,           HeckeOperatorMkZ r	    ʸo,  (                                       0        <   " I L           X   = f h   <    \         	     $               p,     ı  ȱ      q,           M  X H r,           n  ̽  s,                t,           ر  x           ܱ        Ա            H    u,           HeckeOperatorSkZ    v,  (                                       0        <   " I L           X   * g h   )    \         	     $               w,             x,           M sic; ct(Hey,           n   P z,                {,             @                               H    |,  
      
   ReduceCusp /////////},  D                                       0                  $             !    l       x                 
     `                  T           
                  	                    ~,            ,           a sic; ct(He,           d  | | ,           x  S  ,                ,             \        4                    H    ,  
      	   CuspEquiv s(	ȇ	,  |                                     <        $      L       $          p   
     0                                                 $             
                                   	   8              	      ,        X      d  
                                                                                 X             l  (    ,  :    8  A B H  @    h l  9     l  !           !              	           L                   
                                          $            `  8     D     P    `                       (      :      A B   @    h   9       ! t         !              	        P                    $    4          @                  	      p      |      
                                 D   d           	      
                        (         	              4         h      t          i                 \         
                
       
     
                T        (      4    D      i          h          |      
                
       
     
                <                    
                 ,                           \  
 	   h   
 x                         P                            i                              $                      D  	  T        `     p        |         	                                    (	   8          
          	    	      	          	          H	  
    T	      `	    p	         |	      	    	       	          	  # 
        	     <	                  ,        $         0                                      ,                ,        ,                                  <                     ,                ,        ,                                  <        (  ,          ,     8  <  @  D  H  L  P  T  X  \  `  d  h  l  p  t  x  |      ,           N  TW `W ,           a   X W ,           b  HX X ,  
         u1 spEquiv(N,a,b)  /,           v1  4Z  Z ,           u2  p^ \^ ,           v2  \_  _ ,           s1 = Explode,           s2  | \ ,           g  p# h ,           dum 8  ,           r2  x* * ,           r1  ` 8` ,           d a mod g eq,           x0   d ,           y0    ,           x  d = g.  ,           s1p  \ ,                ,                                         H    ,           CuspToFreeHelper    `7 ,                                        <       $       H                           X                     x         0   d                                	                             H  	           <     $              	 0         t     \              	 h                            	                                                  0         <              X     d                   L   `                                                                   	         ,     8    D     T                                                        |         	   	                        (                 
             	  D     P      \     h    t                         8           P     t                                             
                            P      \  !   h  #  x  "         '   D                                                 	                                    8       D      P       \      l         x                          	      ,      	                 j                     
                     	          D      P  !  `       l  '  |  %    
     +                	     8       	   (      8                	                    	!    $  	$   0  	&  @  	%       L  	,   X  	.  h  	-     x  	+         	1     	3    	2        	*               	      	         	         	  		           	             
    ,	     8	    H	         T	             p	      |	     	      	     	        	     	                  	     d	        	  	          
  # j 
  "               8
   
   D
                  	     ,
     |
      
  %    
  )  
  $     
  /  
  -     
      
   
  3                	     p
         
  `
  
       
	 	  	                        
     0    t             	     
     	         	   t   h            j                                           h           L     X                @                           @   |                                                 $        4              \           `      l     x                                                           D                     $        0              L      X       d     t                      
              $     !           &   L        +      .       0     /        ,           : 
 0   6       <   ?  L   <          &            l  !    x  !    !        !'     !$        "      "     "      "     "         "     "      
    #         ! `               @             	   ,          
    T           ,          *
      *      *      *             *	       &            +    +            +  H  +             8  ,	     ,        , ,        h  .    t  .     .          0      0       0$     0&    0%       0#         0)     0+    0*      $  0"               0      0        0
         T  1	   `  1  p  1       |  1    1          1          1     1    1         1#    1          1               2  <  2         $  2    0  2      2    2            `  3    l  3   x  3      3     3         3      3 T          1 H            . \  4           6      6      6
          	    6               ,  @      4         l         4         4                                     3       c                     c   	                                                                            4         4                     ,                           Ĳ  Ȳ  ̲  в  Բ  ز  ܲ              ,  
         M eturn rn   ' ' ,           sign 8 48 ,           a  H9 X8 ,           list | || ,           F    ,           eps   ,           N  4U  ,           k  W W ,           --temp--    '/	'/	/	ʸ,           --temp--    '/	'/	/	ʸ,           i k if we've,  
         b n [1..#list] do  ,           equiv      ,           alp         ,           c ed by the ,           u  d  ,           v  x  ,           g   t ,  
         x  Gcd(N,v);  a[2]; ,           j    ,           i  $[ ,[ ,           ans ` ` ,                ,             t                                H    ,        
   CuspToFree [
	
			ʸ,  0                                       0   =     <   =" k L   =!       d   =%    $   =
      =         = X            >
 	    >                    ,           ,           M    ,           a  D  ,  
         ans m) -> Tup   ,                ,             @        $                    H    ,  
         BoundaryMap ep; 
	,                                        <   E    $   E    H   E     E        d   F 1 t   F          F     F         G&        G'      G)       G(       G+       G- /    G&         G/       G0     G/         G/  <  G             G
  x  G
        0      l  H   T  H       H 	    H	 `      F X               J     J      J     J       J   ,  J            K     K       K     K       K   d  K          X  L 	  @  L       L     L L          M     M      8  M x         N      N      N          
     N      N                  N             N           p	  N        X  O    d  O      O               P      P      P    P        P      $  P           Q)       Q+     Q-      Q,      Q      Q(      8  Q        L  Q	    	    `  Q    
      Q       	     R       R!     R#      R"   t  R      R        R      
     S       S     S      S     S     S        S       <  T    H  T     T     l  T     0     T             T    T             T    T              T      T     T       T       T%      T(     T*  ,  T)       8  T-   D  T/  T  T.      p  T'           l    T$       T       &        X	  S	   X      
     V      V     V          W      W      W!    W          W$   (  W&  8  W%      T  W           l    W        W           X     X     X       X     x   L  X             X    X            X  $  X              X      X    X     @  X     X    X     4            t  Y      Y     Y       Y     h   <	  Y             Y    Y             Y  	  Y            	  Y      Y     Y     0	  Y       Y    Y     $	  &           V	   d       
  O
    L       	  \ 6 	  \	      	  \     \      	  ]&     	  ]'   	  ])    	  ](     	  ]5 1 
  ]4       
  ]8 / (
  ]&      4
  ]:    @
  ];   P
  ]:         ]:  |
  ]     	       ]
  
  ]
        p
      
  ^   
  ^       ^ 	    ^	 
      \ 	  \
         
  `! 6    `         `     `     `         `     
             `    
  $    t  `       @  m    `        ` X          a      a ,    a      h  a          b7      b:      b6               b)       b+     b*       <  b   H  b  X  b       d  b    p  b   |  b    b    #   b        b         b     0             b$            b             b )    b         b                  b1             b       4      b L         c#       c$     c&      c%      c(      c* /   c#        c-      c/     c-         c-  (  c     |       c     c            |  E 0             p  e
   X  e       e 	    e d                  ,  R      $                             $         $                  i                  f                  l                            3       c          c          c             l                             $         $                             $         $          ,     (  ,  0  4  8  <  @  D  H  L  P  T  X  \  `  d  h  l  p  t  x  |    ,           M    ,           Tgens  v ,           Sgens  Xv ,           F 
	
	ʸ,           n   := M`F; ,           i  D" h ,  
         D   := #Tgens;  L ,           j  $' t ,           i   ) ,           uv := Sgens[,           w  8c ,d ,           ind c c ,           g  _ l_ ,           --temp--                   ,           t    ,           --temp--                   ,           --temp--                   ,           x  ;  ,           m if;       ,           V  | | ,           i   \ [ ,           x  $W lW ,           Drows torSpa,                ,                                         H    ,  
         CuspidalSymbols   ,  H                                       <   p    $   p    H   p     p        d   q" n t   q!    c    q        q     X        q     q                p 0                 s
      s       s 	    s                ,        %         %         %      ,       ,           M    ,                ,                              ̳          H    ,  
         CuspidalSymbols [
	,                                         <   x    $   x    H   x     x        d   y n    y         y X            z	      {	      {	           =     |         |           z                 ~ c    ~     0  ~             ~    ~        $        	    `   = p                  T               H  |          x 0   t             
             	                   ,        %                  %                  %      ,        "   Computing kernel of boundary map:    d ,  
      	    seconds.           ,       ĳ  ȳ  ,           M   ` ,           D    ,  
         t  BoundaryMap(M);  ,                ,           س  @           ܳ        Գ            H    ,           Sk ic; ; t),,                                         0    o         	     $               ,       ,           M  d u ,                ,                                        H    ,           IntegralCuspidalSymbols ʸ,                                         <       $       H                d   & f    %          X              n          L               ! 2                                                                                    0       x            l              & a   %         / b   .    /           3      5      3         3      `        ,  9 p <  8    2 L  *       X  E 2 h  D    d x  $    >    #                                        0   t             
             	                       ,        &                             &         &      ,  
                    ,           M  v V  -           Z  g y -           D  P  -           v    -           DofZ  L -           DZ  := [v*D -                -              L   $     ,          8          H    -           SkZ c; ;  Li-                                         <       $              `        0                                                               2 q    1     	                               $          \         L  % r    $     	     @     x             l                                0         t                          	-     c          c          c             (          
-        1   SkZ only takes a ModSym or ModSymFac as argument.    -     0  4      -           M  P H -           --temp--                   -                -           D  P  H     L        @  \          H    -           SkZPlus  "Sk-  n                                       <       $       H                d    g              X             & s    %          ) \                         #      (     '         + t    "     8                            ,       0   t             
   h          	     t                  -        '         '         '      -     P  T  X  -           M    -           S   Ĺ -  
         star  SkZ(M);   -                -           h  P  l     p        d            H    -  
         SkZMinus us; 6 d -  n                                       <       $       H                d    g              X             & s    %          ) \                         $      ) 	    (         , t    #     8                            ,       0   t             
   h          	     t                  -        (         (         (      -     t  x  |  -           M  T< \< -           S           -  
         star  SkZ(M);        -                !-                               ش          H    "-           DegeneracyCosetReps     (˸#-  *                                     <       $      X           d       L      t                     0                                                 8                     
     	 (                            X     d    t      E             L          
    	                                            u                 p  	         D    T         `   u            	 8  	                	                                
      	        D         
     	    $                     t     4        h   
          	     \  v      	     
          	       v           	        
                               <                   l   0               h     t                                                                   ' 
   #         ,  ,  )          / @       L     X    h         t                            	                          ( 
   $          1    .         /                 D   $     
              \  0         
    P  T        	                        	                                 &                           $         ,    H      T     d          p      |                                                                           "     !                           
     <              '    0  0        
       L  	      d              $-        l                           %-                           Ĵ  ȴ  ̴  д  Դ      &-  
         M  step 1. ALENCE:  '-           N  ^ <_ (-           d  p`  ` )-           n    *-           Ndivd et rep+-  
         R  := N div d; idxG0,-  
         max found so far.   --           halfmax d .-           cc H  /-           dd  \	 	 0-           g  P , 1-           bb    2-           aa  T 8 3-           isnew   4-           r  ̌ Ќ 5-           r   h) 6-                7-             X                               H    8-  
         DegeneracyMap  be a 9-                                          0       <      H    w         	     $               :-             ;-           M1  b b <-           M2  0a La =-                >-              |                  `          H    ?-           DegeneracyMap 
	
	P
	ʸ@-  J                                      <   #
    $   #    T   #    `   #   H   #    l   #     #         # 0          $ @    $          $ @    $        $         $           % x    %      0  %             & x    &        &         P  '    \  '     '	       x  (     (     (        ( l        )      )     )        )         - A    -        -          .     $  .     0  . K @  .      L  .   X  .%    d  .&     p  ./ y   ..    L   .%        .3     .4     .3        .3     .         . 	    .       ' D             1       1 
 0  1	       <  1     1       X  2    d  2  t  2         2 
   2         2"     2        2 L        3  Y    3      8  3	           4      4      4     4      4             0  4	        X  55    d  59  t  58         54                5       5#      5&      5(    5'    %    5         5                  5/    L         5             5	   	     P  65 	   \  69  l  68         64               6# 	     6& 
     6)    6(    Z    6"         6                  6/ 
   D         6             6	         <  7     H  7    T  7 K d  7      p  7    |  7     7         7 	    7 0       9      9 
   9         9     9         :      :    :          : 
 0  :       <  :"     :      x  :       h  ;! Y    ;         ;
 \          <!      <%      <) z    <         <
            = j    =      (  =
           >     >      ,  @:    8  @>  H  @=         @9                ?=     |  ?)      ?-      ?0      ?2    ?1    %    ?(         ?     p             ?8    d      	  ?         6    ?         ?                  @4        	       ?       <	    \
  ? T	       	  A7    	  A;  	  A:         A6             	  A%    	  A(    	  A+  	  A*    Z    A$         A     	             A1    	  
       A       (
       A @
       |
  E    
  E  
  E         E                D:    
  C    
  C"  
  C       
  C;        D%      D)      D,    $  D.  4  D-    % D  D$    Z T  C:        C$         C     
             D5    
  d      C         )    C         C                  E    p
         C              C          >   p	      L  G     X  G    d  G K t  G        G      G     G         G 	    G @       I      I               9   L         1                       A-                                                                            B-        9   DegeneracyMap: N1 must be divisible by N2, or vice-versa.  З | C-                $  (  ,  0  4  8  <  @  D  H  L  P  T  X  \      D-           M1   l E-           M2   8 F-           d    G-           N1    H-           N2  8 h I-  
         F 
	
	ʸld t  J-           B  S S K-           D 
	P
	ʸL-           i  ^ <_ M-  
         DB  [d,0,0,1]; olsBaN-           i   p O-           A    x P-           R    Q-           eps 	ʸR-           i  p L S-           r   H T-           RB Trivial(eU-           i    V-           i   \ W-           r  k l X-                Y-           l  @   p     |        h            H    Z-           OldModularSymbols 	x)	ʸ[-                                        0   P x    P         P $         `   Q    l   Q     Q	           Q 	    Q |        Q T                R     R      h  R              S       S      S     S          T {    T     P  T            T     T        D      S    0           V      V     V      ,  V           W      W     W
        X      X&     X)       XK      X              W             \  Z   D  Z    h  Z    t  Z    Z    (   Z
        Z     Z          h |   h        h	          j6 ?   j5         j9 }    j(     @  j         4  j       j     j        (    d  m   t  m        m      m     m         m     m X           n j    n        n            o A    o        o         (  p    4  p" ~ D  p        p        `  q9 @ p  q8       |  q<       qE k   qD       T  q%     q1         qI     q$       q           q       q     q                s-    ,  s1     s,        s         \  u$     h  u1 @ x  u0          u9 k   u8    8   u#         u=     t$       t     P  	    t       t     t            (  p	     <         w  `  w       
  H  w    T  w      w     w        <       h           Z P  x            z
     z      z      z     z    	    z               \-  *      )         )         t         x         )      %             )                    )         )         )         5         )      ]-           OldModularSymbols: NN = ` ^-           is not a divisor of the level = l_ _-                         `-           M  |l q a-           NN   ح b-           N  ܭ  c-           divs    d-           pos , + e-           eps   f-           F   H g-           epsNN  , h-                i-             @          	        ܵ          H    j-  
         pNewSubspace n 0.  k-                                        0    9          l    $       \    x             	 P              @             	             
        
                                       j            	         @     P        \      h      t                            	 4                 ~                       	         H               ,      8   }                      h   1 x                            	            \                           w          D                  (      4    w                     d   c t           ! c                 	     X              l-                m-           ĵ  ȵ  ̵  е  Ե  ص  n-           M  4X X o-           p  Z Y p-           N  ^ t_ q-           k  a b r-           eps @  s-           NN    t-           old  M; P u-           h1 n M;  v-           hp    w-                x-             @          	                  H    y-           pNewDualSubspace 	@	ʸ;   z-                                        0    9          l    $       \    x             	 P              @             	             
        
                                       j            	         @     P        \      h      t                            	 4                 ~                       	         H               ,      8   }                      h       t         w             \                         w          T              X       c          $  6 X 4  5    c D  +              	                       {-                |-                        }-           M    ~-           p  | ( -           N    x -           k  4 8 -           eps   -  
         NN  Character(M); d -           old  M;  -           h1          -           hp  P1 h -                -           $  @           (           0          H    -           Sknew  l(Tra-                                         0             	     $               -     ,  -           M  s hX -                -           <     @     D        8  L          H    -           CuspidalNewSubspace 	ʸ-  P                                       <       $       H                d     t              5 o    4                      X                             0                
              	                        -        *         *         *      -     H  -           M   | -                -           X    \     `        T  l          H    -  
         NewSubspace i j -                                         <       $       H                d    x t                                              
     
                  . x    -        '          '      )   $  +  4  *        &                                   D             `                  x       
     
                X          0   0             $  
             	                   -        ,         ,         ,         ,          -     d  h      -           M sic; ew;  -           p  y  -                -           x  @           |        t            H    -  
      	   Mknewdual  ! " -                                         0             	     $               -       -           M sic; ew;  -                -             @                               H    -        	   Sknewdual ub			ʸ-                                         0   "     !     	     $               -       -           M  0( ' -                -                              ̶          H    -           CuspidalNewDualSubspace ʸ;  + -                                        <       $       H                d   %     $             X                                                          1                              @              
     
        4             X              x         1            3 1   2        &                ! I          L              *    ,  , \ <  )    ^                      l  %    x  1 X   0       $          5     7      6 \              `          $       (     *      ) e    #     @                t          4     d                 X          	                  d       0   t             
             	                   -        +         +         +         +         +         +         +         +          -  
           Ķ  ȶ      -           M  c c -           S ut out the-           p  `] X] -           T  T   -           f   T := Hec-           Ton f := Mod-                -           ض    ܶ             Զ            H    -  
         NewDualSubspace S;  -                                         <       $       H                d   + x t   *        $                                               
                       X          
              $  5   @  4           5 P  0                                         t       0   `            
             	                       -        -         -         -      -             -           M  P ( -           p [pNewDualS-                -             P     	   (          X          H    -  
         ThetaOperator 0.)  -                                        0   # A @   "                  $         p    9                                         8   d                       & A    %               
                                            \   x l         x   x                                        p   P              " j   "        "    $  "      "% j 0  "$        ")    <  "(     "         #      # L             "   X            &      &!     &      X  &           '    '         '     '        (      (      (    ,  (   <  (         ( 	    (       '   H         |  *     *     *    *        *       *
     p   l  *            *     *     *      @  *         $  *   0  *     *         *        `  *      *    *     T             +      +    +         +    +         +      +    +          +    +        +        +
        @  ,    L  ,  \  ,         ,               - 	     -
     -     -	       -	     x   d  -	    
   
      -	    -	       	      -
      -  <  -	            0  -	      -	     -	 $  
  X  -	       -    -     L            , 	   4         /       /# Z    /     	    /               -                                    m         m                                   c   
       -        !   The characteristic must be prime.  Ђ Ԃ -        "   The characteristics must be equal.  Y X -           The levels must be equal.  ^ T_ -           ims     9           std     9             d                |            H    9  
      	   IsTrivial  8 , 9  $                                       <   n
    $   n    H   n   T   n     n     	    n 0                   9  
      r                    9       9           eps esis)  9              9             H                            H    9           Modulus triv9                                         <   s
    $   s       s 	    s 0               9               9       9           eps  : P: 9            D  9             H                            H    9  
         CharacterLevel 	`(	9                                         <   x
    $   x       x 	    x 0               9               9       9           eps  X 9            p*  9             h                               H    9           IsOdd  ; el 9  $                                       0   }  <   }  L   }     X   }     }     	    } $               9       9           eps 88 8 9            \8  9             H                            H    9           FieldOfValues  	 	P(	ʸ9                                         <   
    $           	     0               9              9       9           eps ܚ  9            @T  9             H                            H    9           DirichletCharacterImages } T} | 9                                         <   
    $           	     0               9        m      9       9           eps c; ; ld 9            h  9           $  H   (     ,           4          H    9  
         StandardVector  T 9                                         <   
    $           	     0               9        s      9     0  9           eps c; ms;  9            ts  9           @  P           D        <  \          H    9  
         ImageOrders l Đ 9  ~                                       0     <@       P              $         p      |   #     "            =                 d                             $       (    '         #             8      D    `         ,     p      >            
     T                           
         	                   9                -           i  0  -           R  @ H -           X     -           Y    -                                          H    -           WindingSubmodule  4 4 -                                        0   S
   <   S  L   S          S `         x   S        S    l   S       S      S     S    :    S         S              S $          T      T      T     T      ,  U&     8  U)      U+    D  U*   P  U-  `  U,         U%                U      U     |             U             U             U       U            U     U            ,  T              P  W   8  W    \  W    h  W  x  W    (   W
        W     W          X        X1      X3    X0        X       X           X       X     X              W D            \  Z
   D  Z    h  Z    t  Z     Z    	    Z P                  -        3          0         3          0         0      %             0         0           .           .           M sic; romMo.           i   Й .           i  4N  U .                .                      (          L          H    .  
         LiftToCosetRep   .                                       0   m   @   m      L   m     X   m   d   m  t   m         m         m     m $           m"      m"         m$        m%      m'     m&        m$         m$   L  m          0  n    <  n i    n      `  n     $   t  n          n        0  n
            p     p     p         q      q    q         q      q      q           	    q       p             T  u    `  u     u      |  v       v     v     p            u H             x      x     x        y       y     y               <  x               {     { 0        \      h                P          	              
    	                                        v           	     ~ x       <      H                0        x  	              
    	         l                               v           	   D   X            (  	    4       
                       l      x   i                 `                         
                                       (         4      @                   	                    l                 \  x              .                                                    $      	.           LiftToCosetRep: ERROR!!!  4 < 
.     ,  0  4  8  <  @  D  H      .           x    .           N  X H .           c iftToCoset.           d  ` 4 .           g    .           z1  \ L .           z2  (  .           m = N;   .                .           X  H   \     `        T  |          H    .           ConvToManinSymbol 	p	ʸ.                                         <       $             (  	 0          t      \             h                                     "       !       (     '                 -                   <          P                      |     d               p                #                               #                       ,     8    H         T    d       t                        
          	                       .                          f                  i         c         3       .  
   d  h  l  p  t  x      .  
         M f error   
 |
 .           i           .           mlist   .  
         uv  M`mlist; { & .           w  @p u .  
         R ], mlist); f  .                 .             l                               H    !.           ConvToManinSymbol 	t	ʸ".                                        0    y @           L   ! 1 \                  8   $        $        1 1    0         #                 *       ,    )                                           8      D    T         `     l    |                                              	      
         
    ,               |          
         	                   #.                 $.           M  " \ %.           v  % L% &.           i  ^ ^ '.           x  L < (.                ).             H     	                       H    *.  
         ConvToModSym    +.                                        <       $             (  	 0          t      \   
       	   h                                                   "     !                 '             %      <          P          d            
                        !          x                	                 
       	   4           (                            T     `             |                                                                      (                4  !   @  #  P  "       \  &   h  (  x  '                                                  	     p       H                     "          (     4    D         P     \    # l       |           "     $    #         '     ) #   (       &       !         -     /    .     $  ,       0  2   <  4 # L  3     \  1       h  6   t  8    7         ;     = #   <       :    	   5           0             	        	      # $  
       0    @         L     X   # h         t                                                  
   
      	     	      
      8           (      4     @    P         \     h    x                                             #     %    $                                        
          	                   ,.                          f                  i                   3          c                 -.           ĸ  ȸ  ̸  и  Ը  ظ  ܸ          ..           M sic; ere x/.           i   4 0.           mlist  P 1.           uv  M`mlist;2.           w   ` 3.           ind (  4.           g   ̸ 5.           k st);   6.           R    7.           h  { { 8.  
         P R.1+g[1]*R.2>;   9.           hP    :.                ;.             L                            H    <.           ConvToModularSymbol Symbol(M=.                                        0   
     <              @   $     h        t   ! 1                              '       )     (          /     ,          
      	                      \           	              $           $     l  0      3    `  #   D  /          )                                                          (        P             	     
         
 x       P          T  \       
       x  	                       >.               ?.  
                    @.           M  P	 x	 A.           v  
  B.           i    C.           nz  in M; dsD.           i    E.           x [ <v[i]*x[F.                G.           $  h  (     ,           8          H    H.           ModularSymbolsBasis x  I.  t                                       <       $       H              d   1     p   > 1    =         0                 !        $       & #    %                                     +    X                      P                           D       0   0            
             	                       J.        #         #         #      K.     0  4      L.           M sic;      M.           i    N.                O.           D             H        @  T          H    P.           ConvFromManinSymbol @ H Q.  .                                       0       <       H   "  X   !       d   %   p   '     &             	     $               R.     L  P      S.  
         M ar symbols. s;  T.           x    U.                V.           `     d     h        \  x          H    W.           ConvFromManinSymbol h	ʸ,x[2]); X.  z                                       0    1 @          L               h        t                                	     \        $                 
                                          ,      8  !   D  # # `  "        l  &   T  (    x  '     *    )       $         .          	                    Y.                            c         3           Z.     l  p  t  [.           M  d l \.           uv  ( 4 ].           R rn M!0;  ^.                _.             `                            H    `.           ConvFromManinSymbol     ʸa.                                        <   
    $       T      0                 H           
       
                                   t             
                X             $           <           H       
         0                    x             !           l                	                               $           0    @                h       t   	  \                                P                      
               	       
     	         	              <  !    H  $   T  &  d  %                                "     $ #   #         &    %         (     * #   )         -     /     .       ,  1  <  0     L  +     \  '     l         x                      	                           
                      0         
                 	   	       
   H     T    d         p  "         
            
 <                
   0         
                	   	     '       , O    &     	                   b.  $               c                    3                   d                  d                                   c.                           d.           M   tu e.           P   u - f.           uv  6 \ g.           R   v h.           k  Tz { i.  
         n M`k; st`R; s.} ndij.           ind M`mlist`k.           s  | $ l.           w    m.           ans  valuaten.           x   x o.                p.           ȹ  0           ̹        Ĺ            H    q.  
      
   convergent 	    0˸r.  t                                         	   l   	 $          P   	    \   	
     		         	 D           	      		    	                    		      	     	           	       	    	        	      	  ,  	    	    	      h  	         \  	      	     	     P            	    <        	
 	    	                   s.     й  Թ  ع  ܹ      t.           v sic; alManu.           n  8 , v.  
         i onvergent(v, n) ).w.           x   c x.                y.                               H          H    z.  
         ConvFromModSym  8 {.                                       0   	 1 @   	       L   	     	       h   	    t   	      	       	      	         	 	    	 \     8  	 $               	         	
      	      	      	   ,  	
               	
   <  	          X  	    d  	     	         	      	     	      ,  	 t       	!       	$      	+     	-     	'               	(     	'     	'     	      	    	       	 L           `   	    l   	  |   	         	         	 T           !		     !	           "		     "	           #		     #	            $		   l  $	    	     ,  %	
    8  %	
   D  %	    P  %	   `  %	         %	     %	    
       &	      &	    &	        &	 	    &	         '	      '	    '	         '	 	     '	    '	        '	      p  '	
         D  (	 B T  (	      `  (	     (	        (	 8       )	      )	 	     )	      )	      )	               )	           *		     *	     *	         +		      +	     +	
     D  +	
          +	
             +	
    +	
     X       +	    +	
       x       +	
      +	
     +	
       +	
     +	  d  +	                   ,		     ,	     ,	
     4  ,	
          ,	
             ,	
  t  ,	
     H       ,	    ,	
       h       ,	
      ,	
     ,	
       ,	
     ,	  T  ,	                <  *	   0           .	      .	    0  .	     .	       .	   4	  .		 $        \  /	    h  /	 " x  /	         /	     /	    /	         /	     /	! #   /	        /	         /	#     /	%     /	$         /	(     /	* # (  /	)     8  /	'    	 H  /	"       T  /	-   `  /	/  p  /	.       |  /	2     /	4 #   /	3       /	1         /	6     /	8    /	7         /	;     /	= #   /	<     	  /	:    	 	  /	5         /	  0        p	  /		 P         `	  0	    H	  0	      0	      H
  0		 T	     
  	  1	    	  1	"    
  1	%    	  1	-   	  1	/  	  1	.       	  1	3   	  1	5  ,
  1	4      8
  1	)              
  1	*   	  1	)   	  1	)     1	!       1	
     	           p
  2		    |
  2	  
  2	    :    2	          3	   
  3	 
     	      4	   T  4	 
       
  5	 R  
  5	        5	      5	&    (  5	(      5	   8  5	%      H  5	         5	     5	 
        t  6	     6	        6	 h          7	     7	         7	   	        2	 d
  
         &	      $  
      :	
 	    :	                   |.                                     c          c                      c                     }.                             $  (  ,  0  4  8  <  @  D      ~.           P eturn  .           a    .           b    .           M  ,{ XS .           ZN n M!0;  .           v    .           p  <  .           q ;  inuedFr.           pp  ` @ .           qq    .           ans  ( .           j M!0;   .           det ,  .           g  D T .           --temp--                   .           --temp--                   .           R    .  
         h = M`mlist`R;   .           hP , g[3]*R..           cn  := qq;  .                .           T     X     \        P  l          H    .           ConvFromModularSymbol 	ʸt(v,j); .  x                                       0   @	 1 @   @	       L   @	     @	       h   A	     t   A	      A	       A	      A	         A	 	    A	 \       @	 $                 C	      C	*        C	#      C	%      C	$      C	+    $  C	*   0  C	,   <  C	-   L  C	,      X  C	,    d  C	0    p  C	6     C	/               C	"          Z    C	     	    C	                .                                       c          .     `  d  h  .  
         M eturn ert W V .           alpha   .           beta  p .                .           x            |        t            H    .           ConvFromModularSymbol   .                                        0   U	   <   U	  L   U	       X   U	    d   U	#   p   U	&   |   U	)     U	"          U	,      U	/      U	2      U	5     U	.           U	8    $   U	      U	       U	
         V	     V	  ,  V	       8  V	    D  V	#   P  V	&   \  V	)  l  V	"       x  V	,     V	/     V	2     V	5    V	.          V	8      V	     V	    	    V	
     	    U	                    .             .           M sic; romMo.           Px  4 py .                .                                           H    .           ConvFromModularSymbol  @" .  N                                     0   a	5    <   a	9  L   a	8         a	4              t   a	#       a	&       a	)     a	(    Z    a	"         a	     h              a	/    $           a	          )    a	
     	    a	                    .           .           M sic; FromM.           Px  % L% .           i  c c .                .                      ĺ          ܺ        H    .  
         TestConv \ t\ \ .                                       0   g	-     <   g	: 1 L   g	9         g	,              t   g	        g	        g	" #    g	!        g	         g	     h              g	'    $           g	              g	           h	0     (  h	= 1 8  h	<         h	/              `  h	    l  h	"    x  h	$    h	#    Z    h	         h	     T             h	*             h	             h	           i	       i	 2 $  i	        i	       @  j	       j	      j	 4           p  l	     |  l	9 x   l	8          l	C @    l	B         l	 d       i	   L                .  
                         .        1   TestConv: Modular symbols conversion test failed!  X ( .        "   TestConv: test passed for M=%o_%o
 nversion .     Ⱥ  ̺  к  Ժ  غ  .           M sic; nvFro.           i    .           a lways retu.           i  0  .           b  x 8 .                .         .             \     
     	                  H    .           IntegralModularSymbols  c .  J                                      0   y	 1 @   y	       L   y	     y	        y	 $          z	    l   z	       z	     z	           ~	      ~	       ~	   H  ~	            	7       	;      	=      	<    	:         	6             L  	   4  	    X  	    d  	    	         	   t  	      	      	#     	%      	$      	+    	*       	"        	         	     @             	1              	             	 ,        t  	   \  	      	     	      t  	 h         	      	       	               	      	     	         	                  	               	)     	$    4         	       @    \  	 X          	(      	* S   	'    2    	        	       	     	      	      	         	      	                  	             	       (      	 @        |  	# >    	"       	     p       	     	               z	 x                	
 	    	       	 	    	               .  "      "                  g         h         j         g         i                    "         "          .                        .           M sic;  | .           Q lations.  .           i   T .  
         gens  M`quot;  out o.           n  in [1..#Q.           g  D    .           i  ` \` .           v    .           B    .                .           (  @           ,        $  4          H    .           MkZ c;   .                                         0   	! f    	      	    	 $               .     0  .           M   L .                .           A  
 8
 .           B  
  .           C  P \ .           D  8  .           E    .           F     .           G    .           H   H .           I    .           J  d H .           K   ( .           L  ` d .           M = {@ "A", .           N    .           O   P .           P    .           Q   T .           R    .           S  l  .           T    .           U  p 0 .           V    .           W   4 .           X     .           Y  \  .           Z    .           a  T d .           b  8 X .           c   t .           d  , 8 .           e   , .           f    .           g  |  .           h  4 8 .           i    .           j  ̎ , .           k    .           l  L X .           m   l .           n     .           o  h l .           p  8 @ .           q    X .           r    .           s  p | .           t    .           u    .           v    .           w    .           x   P  /           y  `  /           z    /             h                  (          H    /  
         ToIsogenyCode   /  |                                       0   	    <   	     	          	 	    	 L       	 $   X             	0        	5      	7     	6         	>     	:         	/                	       	     	     	      ,  	" 
 <  	      H  	& 	 X  	%        	         	                   	*       h      	         6    	
     	    	               /              /           ?   T /        $      /           n };  H 	/           i  ` ̬ 
/                /           4             8        0  @          H    /           IsogenyCodeToInteger  ȸ /  R                                     0   	
     <   	  L   	      X   	  h   	     x   	          	        	#      	%     	$        	    	    	         	/        	8      	:     	9       	.    	    	(     	    	 $               /     <  /           s sic; ALPHA/                /           L  L           P        H  X          H    /           SmallestPrimeNondivisor  /                                         0   	"   <   	$     	!     	    	 $                   /     T  /           N sic; s-1)+/                /           d             h        `  t          H    /           SmallestPrimeNondivisor ʸ2); D /  V                                      0   	 9 @   	        	       \   	     	         	 P          	 $   l              		       	 
    	          	     	          	     	         	         ,  	             	
 	    	                    /     l  p      /           N  T x /           p  , , /                /                                |            H    /  
         NthPrime v Dr   /  `                                       0   	    <   	  L   	        	       h   	     t   	     	    	    	 \        	 $               	   0  	            	        	      	               	     	         	        T  	               	
 	    	 H                  !/           "/           n  i  #/  
         p rn PRIMES[n]; y $/           i    %/                &/             L                               H    '/  
         PrimePos ime(p); z (/                                        0   	     <   	     	      L  	 $         l   	    x   	     	          	 	    	          	       	     	        	        	      8  	
            	    	      (  	 	    	         	
           	 `            p  		     |  	     	         	     	        	
          	      	     		                 	 d          	
 	    	               )/           */           p  | x% +/           i  <) D) ,/           ell  i; lc -/                ./                        ļ          Լ          H    //           PrimePos PriP			ʸ0/  ^                                      0   	     <   	 
 L   	       X   	     	          	 	    	 h     L  	 $   t             	+     	*          	      	     	         	                   	            0  	              <  	0     	     	    	                   1/     ȼ  ̼  м  2/           p    d 3/           N    4/           x   \ 5/                6/             \                ܼ            H    7/  
         ModularCharpoly X	8/                                         0   	 a @   	       L   	     	      (  	 $       x   	      	      	     	    (    	
          	     	          	&      	-      	0      	@      	B     	%    	    	        	 l             L  	   X  	   d  	  t  	    (   	
        	     	          	*     	,     	.    	+       	)        	"           	A    	@    y    	9    L    	        	        P  	&    \  	&   h  	'     t  	(     	'        	'     	%     	    	 D      	 @  0            	#     	"     	    	                   9/     %                                                  %                     :/           Modular 4| ;/             </           A  T/  =/           M  XU U >/                ?/             P                                H    @/  
         FactorCharpoly 	*	A/                                         0   	( ^ @   	'        	     	    	 $               B/       C/           A    D/                E/             @         $          H          H    F/  
         IntegerKernel 	5	G/                                         0   	 a    	      p   	 $          `   	 b    	      ,  	 T             	5 P    	4          	$     	#         	                   	)              	              	        	        	         L  	   \  	       h  	     t  	" /   	        	%      	(       	*    	)        	%         	%     	 @          	 c   	    2    	         	            	C   @  	+ R  P  	5       \  	8 , l  	+      x  	:      	;     	:         	:      	     4             	>    (        	         >    	     	    	               H/  
                             I/     (  ,  0  4  8  <  @  D      J/           A    K/           n nteger kerL/           m   p M/           a    N/           d ols(A);   O/           B  ` l P/           b eq(A)]);  Q/           x  p t R/                S/           T  @   X     \        P  x          H    T/  
         IntegerKernel  P U/                                         0   	 a    	      p   	 $          `   	 b    	         	 T            	      	          	        	" /    	         	%        	'      	%         	%   <  	            	 c ,  	    2    	      (  	            	C   h  	+ R  x  	5         	8 ,   	+        	:      	;     	:         	:      	     \             	>    P        	         >    	     	    	               V/  
                             W/  
   `  d  h  l  p  t      X/           A sic;      Y/           n nteger kerZ/           m  s hX [/           B ols(A);   \/           b    { ]/           x  <   ^/                _/                                         H    `/  
         IntegerKernel  % a/                                        0   	   <   	   H   	  X   	    ( h   	
       t   	     	           	 c    	     	    	         	 $                 	 a    	        	              
* P     
)           
      
          
                   
       0       
       L       
      ,   
 d         
     
         
! L   
        
$      
'        
)    
(         
$         
$   \  
         L  
 c    
        
 @        |  
 2    
        
 p          
    
         
     
	          
 	    
       
               
C   $  
+ R  4  
5       @  
8 , P  
+      \  
:    h  
;   x  
:         
:      
                  
>            
         >    
     	    
                   b/     %                                c/                         d/           A sic;      e/           n  \b Xb f/           a  T] <] g/  
         d ows(A); l(A); - h/           B  Y Y i/           K ); ); l_ j/           b  X  k/           x    l/                m/                     Ľ          ܽ          H    n/  
         IntegerKernelZ   o/                                         0   
   <   
   H   
  X   
    ( h   

       t   
     
           
 c    
     	    
         
 $                 
 a    
        
             
) P    
(          
     
         
                  
       0      
       L      

      ,  
 d         
     
         
  L   
        
#      
&        
(    
'         
#         
#   \  
         L  
 c    
     	    
 @                  p/  
   %                         q/     Ƚ  ̽  н  Խ  ؽ  r/           A sic;      s/           n  D3 L3 t/           a  X: 8 u/  
         d ws(A); el(A); 0 v/           B  0= t w/                x/             @                               H    y/           LinearCombinations 	    ʸz/                                        0   

     
	         
 $         `   
    l   
     
	          
 	    
 |        
 T                 
/      
!       
$      
                 
      
    
       $  
    0  
  @  
        
         
                   
       P      
       l  )    
         
                  
*              
         	    
               {/                |/           Comb V W }/           B  X X ~/           n  L[ 8\ /           v  ,  /           i    /                /             \                                H    /  
         IntegerKernelOn T /  "                                       0   "
    <   "
" 2 L   "
!    t    "
     	    "
 $                   /             /           A sic; B[i]*/           B   ( /                /           ,  @   0     4        (  H          H    /  
         IntegerKernelOn p	/                                         0   +
 p    +
        +
 $         `   ,
 1 p   ,
       |   ,
     ,
          -
      -
       -
#     -
        -
          -
(     -
'    ,    -
        -
            .
   (  .
    4  .
    @  .
   L  .
    X  .
   h  .
      t  .
     .
                .
 	    .
       ,
 T               0
8 2   0
7         0
; d   0
1    >    0
     	    0
                   /                /     8  <  @  D      /           A    /           B  H   /           K  of that t/           V nsion(K) e/                /           T  `   X     \        P            H    /  
         LatticeIndex  | /                                    R  4   5
        @   5
) y P   5
(    ,    5
      ,  5
 $             6
 2    6
          6
       6
      6

       6
      6

         6

      6
                   6
    t           6
              6
         L  7
 2    7
      h  7
    t  7
     7

      7
     7

         7

      7
     \             7
    @         7
           (  7
           8
" >    8
!        8

            9
%    T  9
    `  9
 `    9
         9
     H             9
     <  p       9
           8  9
   	        :
 1   :
          :
  1   :
        :
          ;
 	    ;
     l  :
   (      	   \  =
	     =
        =
 P  
       >
' R    >
1    
     >
4 L   >
'        >
6 	     >
= 6   >
8        >
6        >
6    >
    B    >
     	    >
                   /                                      /     `  d  h  l  p  t  x  |        /           V sic; rSpac/           W    /           Vec  lattice/           b  x   /           B   $ /           c  P X /           C  < @ /           Vspace   /           c    /           D  Ԛ  /           n rn 0; 0 /                /             X                            H    /  
         ModSymIsRoot  < /                                          <   K
    $   K
    H   K
     K

     	    K
 0               /        5      /       /           A ITION: erm/                /             H                  ľ          H    /  
         ModSymParent d A`M; /                                         <   P

    $   P
       P
 	    P
 0               /        5      /       /           A    /                /           о  H   Ծ     ؾ        ̾            H    /           IsNew  paren/                                         <   U

    $   U
       U
 	    U
 0               /        J      /     ܾ  /           V    /                /             H                            H    /  
      	   OldFactor    /                                         <   Z

    $   Z
       Z
 	    Z
 0               /        )      /       /           V sic; ew;  /                /                                            H    /  
      	   Dimension   H /  F                                     0   _
#     <   _
'  L   _
&         _
"              t   _
       _
     _
    1    _
         _

     h              _
    $           _

          	    _
                /             /           D sic; ;  /           i  ) ) /                /           $             (           4          H    /           Sha   + /  F                                     0   d
$     <   d
8  L   d
7         d
#              t   d
       d
     d
        d
         d

     h              d
    $           d

          	    d
                /     ,  0      /           D  |  /           i  ,% 0% /                /           @  0           D        <  T          H    /           NumberOfNewforms  , H /  R                                         i
      i
 $             j
    \   k
  l   k
          k
             k
!     k
          k
              l
	      l
     l
                   k
 P              j
    D            o

 	    o
               /     H  L  P  /           D sic; Facto/           i he number /           d  X d /                /           `  0           d        \  t          H    /           NumberOfCuspidalFactors , /  B                                         t
      t
 $             u
    \   v
     v
      x   w
	      w
     w
     l              v
 P              u
    D            z

 	    z
                    /     h  l  p  /           D sic; 1;  /           i ngIntElt  /           d   t /                /             0                |            H    /  
         Wq ic; 1; l(d) then /  R                                          
     
     $           X   
     d   
  t   
         
                 
       
     
          
       
      

                   
    L           

          	    
               /        G      /             /           D    /           i   l /                /             x                               H    /           J0    /  (                                       0   
'   <   
)   H   
, 	 X   
+    8 h   
&        
     	    
 $               /       /           N  % % /                /             `                 ȿ          H    /           SemiDecomposition  |  /  d                                       <   
    $   
   L   
      X   
     
           
    h   
       
     
	           
+        
-      
/      
1     
*        
             

     

             P  
 t              D  
   ,  
       
 	    
 8       
 0                     /                                   /     Ŀ  /           M sic; posit/                /           Կ  d           ؿ        п            H    /           SemiDecomposition 	q	ʸ/  $                                       0   
     <   
   H   
     T   
"     
     	    
 $                   /     ܿ        /           M  @y i /           stop d u /                /             d                               H    /           SemiDecomposition 	X 	ʸop);  /  $                                       0   
    <   
   H   
&    T   
)     
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 $                   /            /           M  pk j /           Vdual  l  0           stop z < 0                0             d                  L          H    0           SemiDecomposition    0  @                                      <   
     $   
"    H   
!    T   
%     
         
 0             
       
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 x             
  A    
           
. 1    
-    ,   
         
             P  
         D  

      
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     
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      (  
	           
      
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	    	   	   H  
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 <  
   
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    
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 k   
         
    
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    (       
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   (  
      <  
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#   P      \  
 k l  
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          
          
     
" :   
        
              
#              
    
            

  T  

    
         H  
   0  
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  t  
     <       

    

    
   h         
    
            

    

    
         
 
      
     
       &           
      
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        D  
   ,  
    P  
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   t  
       
     
%    
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+     
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,     
2    
/         
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 	  0  
       
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     <  
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    
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     
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    
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     
    
       8  
	 8  T           
  X  
     ,       

  |  

    
   L        
    
     p       

    

    
         
 
      
     
       &            
& 
      
)      
6    
5       (  
:     
%      D  
       
     
     8  &          
      P       
     l       
          
    l          

 	    
               0  6                          J                             5                   3                                                  J                    J         5                0          $  (  ,  0  4  8  <  @  D  H      0           M sic; ecomp0           Vdual  ؒ 	0           p  # # 
0           stop Elt,   0           T  c c 0           D stTn(M, Vd0           fac ,1); pac0           f    0           a  h | 0           fT  fac[2]; 0  
         W = Evaluate(f,T);  0  
         Sub se degen maps!! 0                0           X  0   \     `        T  x          H    0           FullCuspidalFactor   h 0                                            

   P   
 $           

     
 D         p   
 1    
           
&     
%    1    
"        
           
       
     
      @  
            
-       
2     
1    \ 0  
,        
#        
          `  
    l  
' X |  
&       
    c   
         
1     
,        
 T          
     
         
        4  
 d          (  

      
       
  T  
            
  x  
       H         

    
     l       
    
              
    
            
     
               

 	    
               0                            5                   K      0     d  h  l  p  t  0           M sic; (~D,W0           W *not* been0           p  ,  0           T  
 
 0           f  Tn(M,p); 0                0                                         H     0           NewDecompositionRecursive  d  !0                                         
               L   
' A \   
&       h   
+ , x   
        
         
   $   
     
 @            
 1    
          
     
          
 	    
      T  
               ,  
    8  
    D  
 W    
        
	          t  
     
         
     
     
        
	           
     
     
      $  
	           
      
     
      `  
	         D  
    P  
 e    
        
	 8  	   	     
       
   t  
    
                
    
            
    
    	           
     
       
  8  

             
  \  
    	   ,         
  |  

     P       
    
    	   p  	     
       
%    
$        
       
            
    
    	          
     
   
      0  

   <  
  L  
         
 4  `      l  
 k |  
         
    
          
          
     
"    
        
               
$      	     
(     
*       
)   4  
$              
           T  
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    
     H  &           
      
 |  
        
     
     
           	                                       :    $  =      9            L   
  X    u h          t  + 	     -      / W   *        #              @             4                     )          <           ,  #     "      x	            \    l        x                                                                           ! 	            k 0         <    L             `       l  !   x  &     )    %        /    ,                            	      
              	                !           0	  	 	      	  d	  	     $	  &           
      
 X	  
         P  <	        
  
	            	   %  	                             	               	  	        t  	 	   
      
   <
                   d
      p
  ;  
  :      
   	   
  ' 1    &          X
           \   L
  
          
  0 	   
  3    
  @    ?      
        /      4                   (  &                @       	 0
  
           
 $  `  	     
    h          
 	                   "0  0                J                             5         K                    K                            K                                           #0        A   Trying to prove irreducible with a random sum of Hecke operators.   t( $0        3   NewDecomposition: WARNING -- space not breaking up.         %0           Newdecomp--recursing with p =    l &0  
      
   and dim =   L d[ '0                                   (0  
         M sic; true; p); e(f)0           Vdual  P *0           p    +0           D    ,0           T rn D; h -0           fac L T .0           f  4 < /0           a  (  00           fT  fac[2]; 10  
         W = Evaluate(f,T);  20  
         appended    30           n  P# X# 40           Tsum nd if; 50           fac2 ' X' 60           WW  end if; 70                80             h                  $          H    90           OldDecomposition 	Ȗ	ʸ:0  0                                      <   #    $   #
   L   #      X   #     #      X  # 0          $    x   $       $     $         %                  %* A    %)          %. ,    %       %        %      %   X  %           H  & x    &        & <        x  ''     '&         '+      '0     '-          '      '                '    l        '             '        '	        <  (    H  (  X  (         (              )#     )#        )%      )'      ))      ),    )+       )(        )%        )%     )      d  ) t         ,  *"    8  *$    D  *'  T  *&    }    *!        *            +!     +         + x           -     .       1"       .     . 	     0> 2    0=         /       /8    $  /: 
   0  /= w @  /7    X P  /)        /         /                   03      `      /       |      .               .      .                  1 
         (  .         )    .     `  .       &             2    2     T       2    2         2    2       t        3    3            3    3         3     3              4  \  4          @  4  P  4         4    4       4  	      5    5     t       5    5         5    5         	     6     6       6  4  6            6  (  6         6    6            X  7    d  7  t  7       7         7   L  7     7              - 	     8      (
    0         :     :         :            ;  @  ;       	     ;     ;        4      $    (            =
 
  p  =       = 	    = |                  ;0  $                          5                              J         )         K         K                        <0                                   =0  
         M eturn if for   >0           D    ! ?0           N  ];  ` @0           a   , A0  
         NN Level(M); ectorSpB0           i ); *  C0  
         Divs n [1..#NN] do iD0           MM  | x E0           DD    F0           A    G0           d  :    H0           b  x  I0                J0           0  @           4        ,  <          H    K0  
         Decomposition 		L0                                         0   B     B     	    B $               M0     8  N0           M   b a O0                P0           H     L     T        D  \          H    Q0           NewDecomposition  X $ R0                                         0   G A @   G     P   G       \   G&     G#          H      H l               G $   x              J       J
      J         J     J      $  J          K      K       K     K        <  L/     H  L;  X  L:      p  L>   0  L      L.       L     d       L    L                M"     M$      M#     M!       M            M     M             `  K             T  O
   <  O       O 	    O H              S0        P                                                       T0        '   Decomposition not programmed in char. p  U0     X  V0           M sic; m ` W0                X0           h     l     t        d  |          H    Y0           FullDecomposition  D  Z0                                         0   V A @   V     P   V       \   V&     V#          W      W l               V $   x              Y       Y
      Y         Y     Y        Y          Z      Z       Z     Z        <  [#  L  ["        X  [;  h  [:    5    [&       [     0       [    [                \     \!      \      \       \            \     \            X  Z   x          L  ^
   4  ^       ^ 	    ^ @              [0        p                                                       \0        '   Decomposition not programmed in char. p T ]0     x  ^0  
         M sic; decomp;   _0                `0             D                           H    a0           GetV ; omp; b0                                         <   k    $   k    H   k     k        p   l   X   l       l      l d            m      m       m       m$ 1    m#        m      (  m            n#      n%      n$     n"        n          H  o  X  o        d  o! 1 t  o         o         p      p I    p        p            q      q!     q      $  q           r      r     r      `  r        D  s	    P  s c    s       s     8             t&   |  t(      t'      t*     t, 	   t+        t%         t          o <          v  ,  v
             v     v               k 0   |           t  x
   \  x       x 	    x h              c0        6         5                                      6         6      d0  
                 e0           A  ` Ħ f0           M  d t g0           V   := A`M; h0           p    i0           T    j0           f  := HeckeOk0           fT     l0                m0             |                            H    n0  
      
   IsCuspidal   7 $7 o0  8                                       <   }    $   }    H   }     }         ~      ~ X               } 0   d              
              	                    p0        K                  K      q0        !   Can't determine if A is cuspidal.    r0       s0           A sic;   llet0                u0             P                               H    v0  
         IsEisenstein % x% w0                                         0     @           
     	     $               x0       y0           A sic; usp; z0                {0                                         H    |0           WqOn ; sCusp}0                                       0    9 @              `          l       T       x          " 
              '     $                    |   $                                       4                d          (      d  *   L  ,    p  +     )                                                  X                                       (   [ 8      X                      t     \                  h   H                                                                         ,       8  ! \                  &          
      H    @                  
 	                &    %        )     ,    (          / 
    1       0  0              	                   ~0  $                G         l         G                   5         G         G      c             G                0  
                    0           A  . $. 0           q    0           r  := [];  0           p  > > 0           w  B B 0  
         --temp--           0                0           $  P          (           8          H    0           SignWN Prime0  ^                                       0   0 x @   /        )       \   2   h   6  x   5     	    '                             "      $     !     
   '           P                  $        @                       
     	     0              0     ,  0  4  0           A    0           fac )  0           p  l% 8 0                0            D  t   H     L        @  p  t      H    0  
         DecompWq 7 8= 8 0  ,                                      0      <     X          $           	                L   d                    
     	                   t                                                    \       $     P        
             D   |         0            !                     , 9    +                                                         D      P   [ `      X          d   8                                                                                 4                    T       (   0                        h                                                        %       '      )     (    \    $     t         &           	   @          
      L            p                  0        G         5         l         G                   G         G      c              0     P  T  X  \  `  d  h  l      0           D sic;      0           M  <  0           i  0  0  
         q `wq := []; o then 0           p    ( 0           w  ,c c 0           i  \_ _ 0           --temp--                   0                0         0                              |          H    0        
   DecompFast  m	m	e	ʸ0                                         <       $       H                           X                     x        0   d                                          	                    "                   H   9            p     X                  d   h                                                                   (       4        "    @  !     L  $    X  ' W                  &            <  |                                   0        L         l         L         L         L         L      c             5          0                 0           A   T 0           maxp   0  
         p st := [ ];   0           --temp--                   0                0         0              L                            H    0  
      
   DecompFast fX		0  `                                     0        <     L                         t        	                                                                                                                   h                 $   4                  0                 0           D   L 0           maxp <  0           NewOnly X| 0           i  ~ ~ 0                0         0             \                            H    0  
         LabelHelper P		0                                        0      <     L                     $           |                  p                  
     	                                                  @                     
   	   4       `      l    |                                                      j                            $      1 4                         .    h  2    t  4    3      \  7      6    1         -                                                   !   ,  #  <                                     (    P  L             h  5                  #                     )      +    *        .       -    ,  3  <  2     L  (     	 d      p  &   X  (    |  '    %         .  P  +         A    @    B   ;         K k   J        E      d  7              (  *    4  ,   d  )            d  0       x  0          
                                                6       5                             5                	      L      X     h      1 x        |                                       
     2 9    1         0      2    1    
     5  (  /     8  "                                  
     H             d  5                            5              @  	     `	     ,             $    4       D              
  `   	  l                   T         H	      	                                   &     #          0	       	                	   $	          	        	  	   |        	   	                x	  &                     	      T  	        
 	     	              0        5                   l         G         G         L                            0                            0           prec _ 0_ 0           D  a d` 0           nprimes \ 0           M  @   0           was   0           i  0 ( 0           j   H 0           j  @  0           t    0           seq | p 0           p  l ȧ 0                0             x     
   $          `          H    0  
         LabelFactors  10^9; 0  Z                                      0     @          L        	            	     \        $   h                                                                                       p                <     H  
  d  	      0               X           j                                                             T                 (  	    4  	A x    	@         	     x     D              $   l                              
           
    	                  
    	      `               4     @    P                   (           "                                                t                                  ' (       8  	       D    T                 p                d                                      	      +  |  (                             ,   	   8      D     T        d        p        #                   	                                                                       	   p          D     T         `    	              	 8  
       !       !    !         !                "      "    "        "      "     "	        $  #    0  #  @  #     P  #        #      |  #	   
      $    $     p       $      $    $
          
    %	      %     %                  "   `       0  !               *   	  * $       P  +     \  +  l  +         +                ,      ,     ,     	  ,             ,      ,
    ,	    	    ,       ,     ,          @	  +    D          .
 	    . 4	              0  "      I         5                                         I                   I         I         I          0        *   Sorting and labeling factors at level %o.
  % % 0     (  ,  0  4  8  <  @  D  H  L  P  T  X  \      0           D    | 0           i rn D;  0  
         M te D[i]`iso;   0           prec & (& 0  
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         was := false;  0# 0           n or duplica0           x  0 0 0           was2 as[1]; 0           i  9 : 0           start  9 0           i = #was+1; 0           E  the entri0           i   @* 0                0            l    p             h        H    0  
         Print  o] := D[i];  0  V                                        2'     H   4    0   4   X   4      d   4     4           5   t   5       5     5         6        7 1    7           7  x    7           7+ @    7*         6	      $  9   0  : 5 @  9W        L  ; 1 \  ;        h  ;  x x  ;          ;+ @   ;*          ;H     ;J      ;I     ;G         9	     x  5              =     =         >      >	       4  ?     ?         @      @	 D       ? (  P          =     `       B      B     (	  4 <               E      E     E        E     E          F! j $  F      L  F    	  `  F, 
  `  F4  `  F% 4  @       F%             F
            G    G        G#     G3    G          G           	  G            H     H           I     I        <  J)     J(         J 0         l  L 1    L         L `       T  I	   L  |        N     O       O< x   O;          OG @   OF         P       P1     P0     0  P#        <  P@ 1 L  P?          PD      O     t  R     S 5   R8         T       T 1   T         T#       T, x   T+          T7 @   T6          TA x   T@        $  U*  4  U)        U         R h       N	   X  D        X     Y       Z x   Z          Z" @   Z!         Z&       [,    [+       [           \ 1   \         \     (  \5  8  \4    x H  \*        T  ]6  d  ]5     t  ]+       ]          ^ 1    ^         Y x      `     a 5   `G         b       b 1    b          b( x   b'        (  b3 @ 8  b2        D  c  T  c    x d  c        p  cH    cG       c=       c0          d x   d          d3    d2        d%         `        X	 l           H            E   t                  0  <                          t         x         |                                                                                                                                    0        C   Full Modular symbols space of dimension %o, level %o and weight %o  z \ 0        D   Full Modular symbols space of dimension %o, level %o, weight %o and   < 0           character %o  %o and " cat  0  
         (plus quotient) Tc 0           (minus quotient) ` ` ` 0           
   _ _ 0                0           eps   0  
         cuspidal   4 0  
      
   eisenstein   \ 0           %3ok%1o%o%1o:  dim =%2o  %10o
   0        "   New %o factor: dimension %o (%o),   ش  0           level %o, weight %o (%o%o)
   0        -   %3ok%1o%o%1o:  dim =%2o  %10o  (old: %3o%1o)
  p{ 0        1   Old %o factor: dimension %o, level %o, weight %o   x_ _ 0           (%o%o --> %o%o)
 ` _ _ 0               0           A  <j v 0           abbrev  L 0           eps egory(A)0           type IsTrivi0           d f IsCuspid0                0         0              $   e  0           Print   ev t0           abbrev      0                                        H    0                                        0   m  @   m      L   m     m	          n      n \          	     o          m $   h            r   H  r                  s      s      s    j   s       s        s         t      t $             s    0          l  v   x  v    v       v         v     v         w   `  w              x       x     x         x              (  y    4  y     y        y              x  x
      D  	     {         v `            ~       ~    ~         ~                                                4      @    P       `         l  "                  !                             |        
             	 (            
            ~                     0                                            e                    0        ,   Empty collection of modular symbols factor.
   0           Modular symbols factors:  T p 0           (nontrivial character)   0        ,   (The isogeny classes have not been labeled.)   0                   1           D if; f; el(1           i )";   1           i  $  1           j  T d 1                1         1              $  $     (          4          H    1  
         NumOldFactors  do s 1  T                                     0        <     L                          t   #       %     $       h   (       '                                           $                        
     	                        	1        J      
1     ,  0      1           D    1           i   t 1                1           @    D     H        <  T          H    1  
      
   NewFactors  ` h 1  L                                     0        <     L                          t                       h   #       "             
                      $           
          	                        1        J      1     L  P      1           D sic;  i in1           i    1                1           `  d  d     h        \  t          H    1  
         NewformFactors  Ⱦ 1  d                                     0        <     L                          t                       h   #       "       )              8       :     9        7         )                     
                     $          
       0  	     H                  1        J      1     l  p      1           D  l x 1           i    1                1             P                   |            H    1  
         NumNewFactors  D  1                                         0     @           
     	     $               !1       "1           D sic; i in #1                $1             P                               H    %1           NumNewformFactors 	p	ʸ&1                                         0     @           
     	     $               '1       (1           D  x4 4 )1                *1             @                               H    +1           newform rmFa,1                                         0             	     $               -1       .1           s    ! /1                01             0          	                  H    11  
         ModularFactor r(s); 21                                            P    $            	       D         p   	     |            :                                                                             !   `      (  %    4  '  D  &      P  - : `  *         !                                   5            	 t                                   0   d                                 P       \    l                                       	     |    p   D                                            (          \                         	 P        |                 :                                                                        $ (  l      4  (    @  *  P  )      \  0 : l  -         $                                   5                      	                          <   p       ,                                   P            4  \                                         
           !       %    $                        0      <                     $                   L             h  6                       "     !         
        <                         ,            	                       31                                                                    41              T. L. 51           0  t3  61           9  6 6 71           k    81                91           0    :1           9    ;1                        <1           s   L( =1           i e the weig>1           sN  - H ?1  
         N le;  cat s[i];  @1           sk  x l A1  
         k while;  cat s[i]; B1           iso   C1           j    D1           sIso 1;  E1                F1              h           $          4          H    G1  
         ModularFactor 	X	H1  $                                       0   '    <   ) 8 L   &       X   ,          	     $               I1     (  ,  0  J1           N  4 <x K1           k  u | L1           iso p t M1                N1           @  \           D        <  P          H    O1  
         ModularFactor 		P1  "                                       0   ' 8 @   &       L   *          	     $                   Q1     H  L      R1           N  Pe $ S1           iso Б  T1                U1           \  @           `        X  p          H    V1  
         ModularFactor 	H	W1  J                                       0                  $         `       l     |           
                                      T                                 	                        X1     d  h  l  Y1           M  `2  Z1           iso   [1           D   0 \1                ]1           |  L                   x            H    ^1           ModularFactor 		H	ʸ_1                                         0       <             	     $                   `1             a1           D  a a b1           iso ` ` c1                d1                                        H    e1  
         Factor or(D,iso);  f1                                       0       <     L                         t   &       -       /     .    :    *          2            6       8     7         > :   ;        2             !       4      @                
 h   (                 $   P      
       l  6                              (    '             	                       g1  
                         h1           0  4 | i1           9  D < j1                 k1           M   D l1           s    m1           i  x 8 n1           t   \ o1                p1             \                               H    q1           Factor r(M,Ir1  "                                       0     @          L   "          	     $                   s1             t1           M    u1           iso   v1                w1                                        H    x1           Factor r(Decy1                                       0       <     L                         t   &       -       /     .    :    *          2            6       8     7         > :   ;        2             !       4      @                
 h   (                 $   P      
       l  6                              (    '             	                       z1  
                         {1           0  S S |1           9  4X X }1                  ~1           D   `; 1           s     1           i    1           t  L} <} 1                1             L        $          4          H    1           Factor r(D,I1                                       0        <                       $     p         |                                                                       	                        
                          L  	    X    t  
      @                                            	    	         h                d   (      
       #   8          		      	 ,                     1        I         I                             1           There is no factor %o.  
 1              <  1     (  ,  0  1           D   l 1           iso  P 1           i    1                1           @  0   D     H        <  T          H    1           Factor e is 1  P                                          
  P        $                     D          
   h                    t                                                                   
 	                       1        5                                       1     L  P      1           M    \ 1           A   d 1                1           `  <   d     h        \  t          H    1           DecompFastTp 	 	 	ʸ1  4                                       0                    $             p   
    X       |                           	     d               1        L      1     l  p      1           A    1           p  T X 1                1             \                   |            H    1           DecompCharpolyTp 	    ʸ1  "                                       0   '    <   )  L   &    ^         	     $                   1             1           A   | 1           p  H 8 1                1             H                            H    1           DecompZ Э 1                                        <   &    $   &
       &	     & 0          t   '   \   '       '     '         (          (.     (-    1    (*        (      <  (            )         ).    )-    1 ,  )*        )      \  )            *   t  * P        |  +    +          +! 1   +         +         ,      ,!     ,        ,             -      -!     -      X  -         <  .    H  .     .        . 0       x  /	      /!     /        /     l            0	      0/ X   0.        0$     `  0                  1&     1(    (  1'    4  1*   @  1, 	 P  1+        1%         1          + p          3    3
            3    3                4    4            4     4            L  ' h              @  6
   (  6       6 	    6 4                  1        5         "                   "         7         "          1                         1           A    1           M     1           Z  0  1           Zdual  x 1           p (Sk(M))); 1           T    1           f    1           fT     1                1                                         H    1  
         DecompZdual al; " 1  :                                       <   ;    $   ;    H   ;     ;           <     <     X   r           ; 0   d              >
      >       > 	    >                    1  
      7         7          1       1           A   d* 1                1             d                            H    1  
      	   CuspOrder   1  $                                       0   H    <   H   H   H    T   H"     H     	    H $                   1  
                          1                1        1                                  <                    1                1        1                                  <                    1       1           A CES: al;  1                1           $  d           (           8          H    1  
      	   CuspOrder  X? \? 1  $                                       0   N    <   N    H   N    T   N!     N     	    N $                   1     ,  0  4  1           A sic; rder(1           alpha  $A 1           beta B B 1                1           D  L           H        @  P          H    1  
         TorsionBound R	R	1                                         0   U   <   U     U     	    U $                   1     L  1           A    1                1           \     `     d  	      X            H    1  
         TorsionBound  l 1                                        0   \ @ @   \      L   \  \   \          \ p          |   \1 j    \0        \&         \             \ $        ]       ]      ]                ^ 9   ^          ^ $  x      0  ^$ x @  ^#       L  ^+ 
 \  ^'       h  ^0  x  ^-         ^               ]
      ]                 ]              ]           <  ]            _      _   $  _      0  _     _          b     X  a0    d  a2  t  a/          a8    a7    \   a,       `:         a=     a? 	   a>        `!         `     L             b    @         `            `         `
 8           dE     t  d3      d6    d2         d9     d; 	   d:        d!         d     h             d@    \         d            d         d
        p  _   H  (     `  f     f        f	 T           g k   g
         g     g         h     h        h      h!     h     E   h         h         h     h         L  i   X  i  h  i       t  i     i        i @        j      j          g   ,           l
       l 	    l                   1                1     h  l  p  t  x  |        1           A sic; onBou1           maxp   1           p    1           S    1           p )),p+1)   1           seq   1           p  7  1           bound  ) 1           b  X* l{ 1                1             @     
     	                  H    1           ScaledRationalPeriodMap ʸ`l	ʸ1  8                                      0   w 1    w      (  w $            x     x   x    `   x"       x!   l   x$       x#       y        y y    y    /    x         y        y# 2    y"        y        y X    x      p  x T          T  z   <  z    `  z g    z        z H          { 2    {         {      {     {         {                  {             {             {	        8  |# R  H  |-       T  }  d  }       p  } /   |#        }       }!     }         }  S   |    2    |        | ,           ~)       ~       ~	                  ~$              ~	            h  ~   P  ~      ~   \  ~      ~      ~ , 4  ~      |  ~ t                            	                      ! / ,        8  #    D  $   T  #      `  #  l  (     &                                   	                   1  "                 5                  5                    5                             5                   1                       1           A     1           d used inter1  
         P imension(A);  Ȋ 1           Z  b b 1           z  \ \ 1           PofZ _ _ 1           B = [z*P : z1           b    1           I  P ( 1                1             |                             H    1  
      	   CuspOrder  D T 1                                        <       $       T      0        `      l   "             
     H    4                                                                h           (                             \      h    x                                                                                   $  !    0  '   L                                 
 P           #   |  %      $      ( Z    "        
                  '    &                
   	     (  ( 	   4  2 y D  1         '          	   l   
   x                            `             " 
                             	                   1        5                           5         3          5          1         F ng1        1                                  T                    1           X  D: : 1           Y   ( 1                            1           A sic;  xSpa1           alpha  40 1           beta 3 8  2           i  H5 T5 2  
         R 	 	ʸ`l	ʸ2           X  D: : 2           Y   ( 2           modsym  | 2           v  Z \[ 2           w  p`  ` 2           i    2                	2           ,  @   0     4        (  X          H    
2  
         ModularKernel   2                                         0    r          p    $          `                 	 T                 
                                 	          4                              $  + 1 4  *    L D          .    \  * 2    )       x                      	     l                 P         9 2    8        .            	           (  .         .   d            T             \   H            @          *      3 b   2         )                                                           $                    (  	     x                  2  
      l                     2     8  <  @  D  H  L  P  T      2           A sic; Denom2           Z   $ 2           Zdual Z(A); 2           w    2           v    2  
         D rn 0,[];  hen  ); 2  
         S  Basis(Zdual)];  2           i   X 2                2           d     h     l        `  t          H    2  
         ModularDegree  D 2  D                                       <       $       H                d                      X                              0   t              
              	                    2        =         =         =      2     p  2           A sic; minan2                2             L                |            H    2           CongruenceR 		`l	ʸ 2                                         0       <              |    $          l    ?              `                                       <       &     %          )   T       .       0    ,  /     8  7      9    D  8  T  4         )            t  -      /     ,             h             7                      6                 t                0         <       
      X         	     L         d                 # 5                	                       !2        I         I         l      "2  
                 #2           A    $2           prec  4 %2           Q1 n prec.} &2           M    '2           D   h (2           B   x )2           Q2 llDecompo*2                +2                                         H    ,2  
         TorsionQuotient  -2                                        0      @           L   * 1 \   )        h   4 y x   3    /             7        > 2    =         7         7       $                       T                 (  ' a 8  &       D  0 b T  /     d                           7      9      ;    8        A     >                                   
                             
          	     8                  .2                /2                 02           L  P  12           D te abelian22  
         S e(L))!Basis(L); 32           i   3 42                52             l                               H    62           AbelianIntersection % $! 72                                         0    ? @          L   * ? \   )              P   $                                             *     )                                            (        4         	            |   @          t   r             h           r                                                H            ,         8                     d      p   	             X                
           	                       82               92  
         A eturn m(D); nteger:2           B  '  ;2           ZA  | 6 <2           ZB  8 8 =2           Z  A A >2                ?2             @                   X          H    @2           AbelianIntersection  	ʸA2                                        0   
     	         $        `        l   #                                       r             	                       T           	            \            0     <    L      y             $        |     ,          =      @      <               .      1    0    1    -         #                  7          H  #         ) X  !       d  $   p  &    %         )    (    /           +      ,     +         +   ,   p                        2          H          L      X    h                                                           	                              	           
              
 	              @  0     l  	  |           	    
         `  
                                                                     8      D    T      2             ,                                                                                    $               |         
   T      `      l   	                  H                              ,         
                   	             	                      t        4  
  h  	                \           
    x  D                                <        d                       ,      2          	          \      h    x                                                                                 T	         
   ,	      8	      D	   	            
        	   	  
      	  
  	                  	         	      P  l	     	             D   	        
       
  ' a (
  &        4
  0 b D
  /     T
                          |
  7    
  9    
  ;  
  8      
  A     >        
      
      
                
 p
  
                  
  
       
         	     (                  B2                C2                $  (  ,  0  4  8  <  @  D  H  L  P  T      D2           S    E2  
         n lar factors.} eticF2           i    G2           ZS ; g  d H2           m     I2           i  @ D J2           D egree(ZS[1K2           B //////////L2           i    M2           c  | t N2           s    O2  
         t +1;   := B[i][c]; P2           j    Q2           i    R2           c    S2           i  L~ ` T2           c  \ f U2           i    V2                W2           d  H   h     l        `            H    X2  
         PeriodIndex * , Y2                                        <       $   
       	       0                t                  h                                      \                                              (   1 8         D             `   R  p        |                       	     T                                     @              1 $         0             x        \      h            	     P              Z2  
      5                     [2  
   p  t  x  |        \2           W sic; i] : ]2           A    ^2           Plus c 0d _2  
         M PlW	X	O	ʸ`2           S  ] ] a2           LW  \  b2           LS    c2                d2                                         H    e2           PeriodImage g	g	O	ʸf2  <                                      0    1 @          L                  "                  #       "   \    " >     !     	      x     ,   $                " 2    "         "    "    P   "        "        "          L  #" R  \  #,        h  $& 1 x  $%         $* /   #"        $,       $3 2   $2        $,        $, S   #    2    #        # @          %$ R  (  %.       4  & 1 D  &       P  &  / `  %$      l  &"    x  &) 2   &(        &"        &" S   %    2    %        %            '&      '      '     '         '                  '!               '0     '+    @  (       '       L    ,  ' d         ( R    (!          (&    (%         (*    ()    /   (        (.      (/      (.         (.     (         L  )    X  )     )       t  * 0    *     	    * h      ) @             , S    ,     	    ,               g2                                      h2                         i2           W   й j2           A  ` l k2           n   3 ,3 l2           Phi   m2           y  _ _ n2           x  ^ ] o2           PhiW [ <[ p2           MatW b  q2                r2             L                               H    s2           LRatio      t2                                         0   1   <   1     1     	    1 $                   u2       v2           A    w2                x2             H                            H    y2  
         LRatio o(A,1);  4 z2  x                                      <   9    $   9
       9	     9 0        h   :    t   : :    :          :             :        :" @    :!         :%     :$    :    :         :             :        ;    (  ;   4  ;     @  ;- @    ;,      t  ;               <      < h             : \   P            >     >      >     >        ?*      ?-     ?/      ?.     ?1  $  ?0         ?)            L  ? R  \  ?      h  ?  t  ?     ?         ?      ?     @             ?$             ?             ?            ?     ?            `  >           <  A      A   \      h  A 	  P  A    t  A      A    A       A    A         A               B @    B        B           D'      D)    D&        $  D-    0  G  @  G          G T  p     `  G!  p  G         G              G%          G0    G/          G3          G=    G<        G3             G%             D     H  C       
  <  C       C     C        0      A 0              J
   x  J      J      J     J    	    J               {2  (      5                                    D         3                     D                   D         D         D          |2           LRatioOddPart: s =  |  }2              k =   ~2        H   However, s must be a critical value, i.e., an integer between 1 and k-1.   t 2                2           A   X 2           s  |	 	 2           M dd, and th2           i   p 2           k    2                2              L           $          ,          H    2  
         LRatioOddPart   h 2                                         0   P   <   P     P     	    P $                   2     (  2           A   T 2                2           8  t   <  '   T        4            H    2           LRatioOddPart 			ʸ2                                        0   l  @   l        l          m      m P              l $   \            o       o :    o          o            o        o" @    o!         o%    o$    :   o      0  o             o      L  p    X  p   d  p     p  p- @    p,        p @              q      q              o                t     t
       t	   `  t          $  u     u    0  u     u      X  v%    d  v(   L  v*    p  v)   |  v,    v+         v$              v      v                  v    @         v             v     v      v  H  v            v     v        <    `  u   (            x 	  x  x      x      x    x       x     x          y       z @   z     x  z       {    $  {   0  {  @  {       {     \  }    h  }    }       z#   P      z#             y        y                                             H           ,      8   y H                        p      |                                                                                                 	 d         H  
       0     l  	    x                            
                                       B                     0           <   ( L        X                          h                                                                           	          l  	 $  t         @     L    \                @   4  	   	      (                                           	                    D	     
      (	                     	   	     R  h	  -    
   t	  1 ,    #          X	     	   	              	   	        	   y          $
   	  
   R  
  -    
   
  1 ,    #      T
   	     	   D
  %     $      \   8
         
     h
      
              
  & Q    %      
   
         
  &    
  (     %      $   
         B       E      A            H  '    T  '   `  (    l  5    x  7    4        (        (  	        $      $     %      ? 
     B     D    C         >             0  3    <  5     2         &     $             9      L      &       h      %        %  
         "     <             <            "             !     D                           8    ,   t
  
            
          !                            4      > y   =         3                          ,  !    8  "    D  &  T  %      d  !      p  !    |  )                                .                                                 t                                 	     	     d     p   
                                                     g       2          P              &   (  B 
   4  E      A             \  1    h  3    t  6    5        0         (     P             <             (              $                  !          @  $              %     #     p       4                    d                                                                             g (      2                        (   d  A 
   p  D      @               0      2      5    4        /         '                  ;    X         '              #                  #    L       |  #      <     T  $     "            p                              8                                        	 X         D       P  !   8  #    \  "  l         x  ,     *            ,               0                                                            <                                  P    |                     p                                 ,     +     \         ]          $   !        0      <            `                                  t  "                               #                        1     0              ]           	   (  L        `          x                $  x              )    (                      %             L                $  
 &        0      <           	                       2  x      @         D         H         L         5         E         3                   E         E         E               %             E         P      %             O         O                               O                    P         P         P         Q         Q         Q         O         E         E         E      c             E         E      c             E         E         E      2        "   LRatioOddPart: A must be cuspidal.  (  2           LRatioOddPart: s =   T 2              k =    2        H   However, s must be a critical value, i.e., an integer between 1 and k-1. , t p 2        0   LRatio: warning L-value only up to =/= 0 scalar.  0 $ 2  "   X  \  `  d  h  l  p  t  x  |                                              2           A  ,  2           s  4 P 2           M  ' |; 2           i           2           eig + + 2           w      );  2           eigw 8 D8 2           i  l9 t9 2           Nrm RatioOdd2           Q  4 0 2           n  P H 2  
         vi  n        := 1;  2           V   vi      2           g    2           R    2           sturm    2           f      sturm2           j    2  
         h  in [0..n-1]]  2           i    2           i ]] : 	P	2           j    2           Z    2           z 1..n]] :  2           i     2           VolL y  2           z     2           i  $  2           --temp--                   2           --temp--                   2                2             @          
                  H    2           LEpsilonVanishes 3	    ʸ2  $                                      0              @   $          `    @ p         |                               0 j    /        %                               4 0          A     @     0  7      D  4                 X     d    t                                                9          	                           (                                   t   T            d   <             X            ?                               1       ,                                          <  D    H  G   T  I  d  H         C                                                                              \  #    $  6  4  5        8     %             h  2   x  1        %   @  %    "                     !                           >    0                 )                      L      X     d      p                              @       D     ,                                       ( $  
      0               L   2          h      t                                !        B       
    (    ,    *        %          	            	 \            
    @  (      d   2        	                	                                     #          
      	            	 t            
 	   X      h     @  ,       
 	     \              2  (                                                                 %   V                                                                 2        7   Currently only implemented for new factors A of J_0(p), 5 2        !   and for eps a character modulo p.  x ,7 2                              2           A    2           eps T , 2           p    2           F  8 d 2           M  4 ; 2  
         V dSymParent(A); ); 2           a  4_ L_ 2           e  Ђ Ԃ 2           b  4  2           b    2                2           $  @           (           <          H    2           LEpsilonVanishing  x  2  p                                       0              p    $         `    9          t   T                                              +       .      -           7   *                  	                              $              @       X           
 	                       2     ,  0  4  8      2  
         A sic;    b		2           p he degrees2           d  P ` 2  
         v IsPrime(p);  8 2                2           H  L           L        D  T          H    2           XGroup      2                                         0      <             	     $                   2     P  2           p  <  2                2           `  4   d             \            H    2  
         XGroup p(p,1);  Nero2  L                                  =               $          T    9 d                                   #      &       t               H                                        T            (    8        D  "  T        h                                   &     (      ,     .       7      9    6         <       x                                 <  	   H             d        p  !    |  !        !       	 X  	    #        #D      #	        0      =     %         %        <   $               '    ,  '     '        '        `  (       l  ("   x  ($     ('    (#    b   (!        (        ( P           )
    )       
     )  X  )               *    $  + = 4  +         +      +            |  *   @             -    -     p       -    -               .    .            .    .               /
 	    /                   2  .      h         l         p         t         x         |                                             Z                  2          5          2  
         CharGroup:    2           p =    2  
          is not prime.  L 2  
         CharGroup:   D 2           (p,M)=(  2           ,  8  2           )=  h  2           >1.    2        7   Computing character group of torus of J_0(%o*%o)/F_%o.
  2        /   Computing character group of torus of J_0(%o).
  2  
      	    seconds.  0  8  2  
                   2           p   , 2           M    2           tm NOW RETUR2           t  of torus 2           B putime(); 2           X andtModule2                2             H                            H    2  
         XGroup_p * * * 2                                         <   4
    $   4       4 	    4 0               2        2       2       2           X sic;  & 2                2             H                            H    2  
         XGroup_M  1 1 2                                         <   9
    $   9       9 	    9 0               2        5      2       2           X sic; racte2                2             H                 ,          H    2           TXn c; el M 2  `                                      <   A    $   A    H   A     A          B	   p   C	    |   C=      C? m    C<         CD      C	 d            0  B X                 E      E       E      E#     E% m    E"        E     P  E             E    E        D     t  F     F m    F       F     h       F     F               G       G     G      G     G
         H       H   ,  H  <  H    D L  H    	    H        H            I	     J	      J9      J<     J	 |         =     K         K        4  I p              M 	    M      M    $  M     M     T  M        
     M    M        H        N	     O	      O& =    O%         O	 x             N l             Q      Q m    Q       Q            Q     Q               G   \          A 0      0      x  S   `  S      S      S     S        S     l     S        X  S           T     T          T* b   T)    L $  T      0  T-    <  T.   L  T-         T- 	    T               2  0      [                            Z         [         \         \                           Z         [                  \         [                 2        -   TXn: Computing q-expansion of theta series to  B  3            terms.  3        -   TXn: Computing q-expansion of theta series to  8  3            terms. d 3           finished.  Time =   B,m);  3  
            $  (      3           X  9 9 3           n  : : 3           m    3           t es to",m, 	3           T    
3           W  < 4 3                3           8  L   <     @        4  \          H    3           MonodromyWeights    3                                         0   Y   <   Y     Y         Y	 $          x   Z	    `   Z       Z
      Z l            [      [     [         [            [        $  [           \)      \2 b $  \1         \(            L  \   \  \      h  \    t  \      \      \    \        \    \        \         \      \
     @             \#              \
         	    \                   3  
      [                     3  
   D  H  L  P  T  X      3           X  D < 3           dummy m   3           TM ined.   3           T `TM; (X,2)3           W    3           i    3                3           h  L   l     p        d            H    3  
         PhiX_and_mX   3  8                                      0   b   <   b     b         b	 $          x   c	    `   c       c
      c l            d     d    y    d         d             e 1    e      0  e            f      f     f      D  f
        X  f          f          x  g     g    g        g        g l         h      h      h"    h!         h               h 	      h # 0  h       <  h    H  h # X  h        h         h	                  h 	     h       h	             h   
        i 2    i        i       i     i      i   (  i         i      i	                  i      4       i	       P    0  i h         j"     j+         j.     j0    j/         j2 /   j"        j4 
      k6       k+    (  k    4  k!     k         k                  k&      D       k       `       k     x             k1            k         6   k
        j4        j4     j    P    j        j        P  m    `  m)       l  m, L |  m       4  m.     n      n     n    n         n               n      n     n         n	                  n           P  n	           `  m.      l  m.  |  m        l        l D         o%     o.         o1 L   o%      p  o3       p(      p      p     p         p                  p#              p0     p+    L  4      p       X      o3        o3     o        o           q      q    q        q        q        $  r   4  r      @  r    L  r   \  r      h  r   t  r#     r#        r%      r&     r%         r% 	    r               3        [                                                                        3     t  x  |                                            3           X sic; gers(3           V  @ 8 3           dummy    3  
         TM ined.   V.}   !3           n `TM; (X,2)"3           m    #3           T1  X P $3           W1  Ƚ Ľ %3           L    &3           i           '3           B atticeWith(3           v  @ 8 )3           C  ( $ *3           u  T P +3           v     ,3           S  L!v : v i-3           i  p Tt .3  
         PhiX  B ]) );  ܦ /3           v  k k 03           u   Ȃ 13           disc i] : i 23           mX  5 @ 33                43             \                               H    53  
      
   XDimension   p  63  "                                       0   y   <   y  L   y    b    y     	    y $                   73       83           X sic; ers()93                :3                                          H    ;3           XGroup (TXn(<3                                        <       $       H                d       p             	     X        0                                         
                                            0   9 @       P              p      |  #   d  %      $      '    "        -    *                                            $            (  '     )    4  (     &       P     \                
     D                   l       
 0                                                '     (  9     ;    4  :  D  8     T  *         &                           p             !      |               {           
                             T              8      D                ,            	  h                      (   
    
                       !     !        #        %     '    ,  &    8  )  H  (      X  #      d  #                       	       
     	               t  t            
                           	                   =3  0      3          3                                                2                   2         2      %                                  2         2      >3           XGroup: the weight must be 2.  $ ?3           XGroup: invalid value of p.   @3  
                   A3           M rn .}  B3           p  ,c c C3           x  @ ` D3           fac "XGroup:E3           i   < F3           i   ܦ G3                H3           (    ,     4        $  @          H    I3           XGroup ];  J3  \                                       <   "    $   $    H   #  X   !               t   	           
                                                        	    	          h           <      0           	       0                         K3  
                0          L3           N has no square free divisors.  @  M3     8  <      N3           M  Z Z O3           x results.} P3                Q3           L    P     X        H  d          H    R3           XGroupV no sS3  \                                       <   "    $   $    H   #  X   !               t   	           
                                                        	    	          h           <      0           	       0                         T3  
                T          U3           N has no square free divisors.  
 V3     \  `      W3           A     X3           x    Y3                Z3           p  X  t             l            H    [3           XGroupV no s\3                                        0     @        P                       |   "    d   $       #   p   &       %      +     (                               .              <    ;        2         .                     4              $   @                     |                       p                                 (  '       9     ;    4  :     =    @  <  P  8     `  *         &                           |             !                     {           
                             x               P     8      \      h    x      (   
    	                    
                           4                     -  $  ,             `           T  	       
    	        H        #     "         x             d                                       1          $  !            @      L                4         |        "           4   p                                         7      9    6     $  -             `           T                     H                  L   x                                                              4                        (              	                 \       D              
                          	                   ]3  :      5         3          x                   2         5                   2         2      %             5         2         2         2         2         |                  2          ^3        9   XGroupV: weight must be 2 and A must be cuspidal and new.    _3        3   XGroupV: Warning -- space taking more than 23 Hecke    `3        !            operators to break up...  0 8 a3                         b3           A    c3           p    \ d3           i en   e3           j   Ė f3           Z  4 < g3           d     h3           T    i3           f  L  j3                k3                                        H    l3  
         PhiX ; ]; Prime(p); m3  \                                       <   "    $   $    H   #  X   !               t   	           
                                                        	    	          h           <      0           	       0                         n3  
                          o3           N has no square free divisors.   * p3             q3           A  1 1 r3           x  H L s3                t3             t                             H    u3           PhiX ;  no sv3  v                                      0     @                            P               $   \                                                                                                  <     $      H               /     |  A   d  C      B   p  E      D    @       2         .               !                         )    X      8            {         h                           \       0  H                                        L               	                  ,      
  8               T    d      9              6 ?   5       (          G    F                     t     	                         $     &    ,  %    8  (  H  #        T  4    `  6  p  3                          	                       H                                   4           (                                         |  
   d                            	     p              w3  .                                  N         5                            N                   N                  5         N         N          x3  
         A must be new.  4 y3            p must exactly divide the level.  l: p: z3             N   {3        |3                                  <                    }3             xdat~3        3                                  <                    3  
                   3           A  . . 3           p  / / 3           i  PA XA 3           i  L D 3           x    3           y  d \ 3                3           (    ,     4        $  @          H    3  
         XModularDegree ; ;  3  \                                       <   "    $   $    H   #  X   !               t   	           
                                !      #     "             	    	          h           <      0           	       0                         3  
                0          3           N has no square free divisors.  0 3     8  <      3           A    3           x     3                3           L  X  P     T        H  d          H    3  
         XModularDegree 		3                                         <       $       H     X               x             l                  /        1      3       2     .         7     %          =    :                      (      4                           0   D            
   p                                            #         	     |              3        N         N                   N                3     X  \  `  3           A    3           p    3           dummy   3                3           p  @   t     x        l            H    3  
         PhiX_and_mX p		3  @                                      0   
 y    
      p   

 $         `    1             
 T                          
                   #          & L             (      )     (         (     
         @      L                     t         (     '            h                                   4                      
          (    2          D      P     \      h     x                      8                                       
   	          2                     (   
   4     D                                    
     P              l    L  
          &     /         2     4    3         6 /   &        8 	      <       1    D  %    P  '     $              8             ,    ,  `              |                         7                       6            8      ,  8  <      P            
        l  (   |  1         4 L   (      P  6     !      $     &    %                                                                          l         8    |  6        6                    
 `         '     0         3 L   '        5       (          $                                  #       4        0     +    h  P             t      5        5              
                                       
        @     P        \      h     x               #     #        %      &     %         % 	     4                  3                                                                                                 3     |                                          3           X    3           V  P D 3           n  $  3           m  Ի ̻ 3           weights T 3           W    3           i := MatrixA3           L    3           v  \ X 3           B := Lattice3           v    3  
         C move to L!   3           u    3           v  \ X 3           S := [ L!v :3           i     3           PhiX  ]) ); 3           v    3           u  p Tt 3           disc        3           mX    3                3                                         H    3  
         MestreGroup Xf ̨ 3  t                                       0     @ @          L                    !      ! \                 $   h              #     #    9    #      l  #           $      $       $     $          %#  $  %"       %     T  %            %     %        H      $    4            '
     '       ' 	    '               3                 3         3         3          3           MestreGroup: weight must be 2.   3       3           M sic; ers()3                3             8     	             (          H    3  
         MestreGroupV 		3  v                                      0   /  @   /     P   /         /    d       p   /, @    /+         /2     //        /!         /              /5              /D     /C        /:         /5               0      0            |  / $              \  2  l  2    9    2      p  2 P        3     3      3     3          4$ ?   4#        4      <  4          5!         5+ y ,  5*        5     \  5             5    5        P        6#     6"        6 t          7   \  7            8     8      8 1   8         8#     8           9    ,  9    9        9        \  :   l  :%     |  :        :(       ::      :=    :9        :(         :(   L  : P           ;     ;      ;      ;3      ;5  ,  ;2    c <  ;)        ;     l  ;            ;
    ;
        `       <     <      D  <           =     =    =          =          =      =              >   4  >               >?      =	              8   <      3               B
     B       B 	    B                   3                 3         3         3                    3         3                  3      3        >   MestreGroupV: weight must be 2 and A must be cuspidal and new.   3        /   MestreGroupV: Warning -- space not breaking up. V 3  
              $      3           A  (b b 3           Z  h 8 3           d    3           p (Z)); ̿ 3           T  ز  3           f  := TpD(Z,3                3           4  |           8        0  @          H    3           MestreEigenvector  ^ x^ 3  *                                       0   G5 ? @   G4     P   G'        \   GG  l   GF       G     	    G $                   3     <  3  
         A sic; tre; ime(p); 3                3           L  0   P     X        H            H    3           MestreEigenvector  \  P  3  l                                       L      L $          P   M    \   M l   M       x   M \    M         M D            N ^    N      `  N             O    O        O	         P     P      t  P          4  Q	   @  Q     Q          R      R	 P             Q (  \          T     T 
    T u   T          T&      T(   T%         T+ \   T!        T     L  T                <  U ^    U         U 0         O          W! R    W+         W4 b   W3    L   W!        W7      W8     W7        W7      W:     W      X  W t        ,  X   8  X  H  X        X        X          x  Y      Y y   Y    ,    Y      p  Y l          Z 2    Z        Z	      Z	     Z
      Z     Z
         Z
      Z                  Z              Z       <      Z T  	       [ 	     [#    ["         [               [ 
     [    [    	     [ 
     [    [        [         [                  [ 
     (    x  [       D  )    [
     	    [ \              3        T                            3        &   Couldn't verify that V is irreducible.  D 3     \  `  d  h  l  p  t  x  |      3           X sic; eEige3           V    3           p    3           T    3           f    3           e le; ularCh3  
         F s(T))!T,f);  4 3  
         W rent(e[1]); trixAl3           b   Ė 3           B  d t 3           i    3                3             @                               H    3  
         MestrePowerSum 	`S	3  ~                                       0   b    b         b $         `   c y p   c       |   c     c        c        c T        d!       d%     d$         d                 d      d    d       $  d  4  d       @  d    L  d  \  d        d         d                   d       l      d         )    d
     	    d                   3               3           X  \ ̪ 3           e  L X 3           n  ` h 3  
         w :RngIntElt) -> .  3           i  T  3                3                                         H    3  
         MestrePowerSum 	(]	3  J                                       0   m  @   m    9 P   m        m          n      n `               m $   l              p2 ?    p1        p$           q+    q*          q.    p     	    p                3              3        %   Currently Conductor(A) must be prime.    3             3           A  @  3           n   x 3                3             @                            H    3  
         ComponentGroup   3  f                                       0   }     }      D  } $       h   ~"    P   ~$    t   ~#     ~!        ~          	           
                                !      #    "            	    	                    h  ~    \   ,       	       \                     3  
                          3           N has no square free divisors.  . 3             3           A sic;      3           x IsNew(A); 3                3                                4          H     4  
         ComponentGroup 	 	4  T                                     0    9 @                  \       h   )      ,       P               $   t               x                                            	                          D     ,      P      \    l        x                      N                      	            8                               D            4            T   (         p     X      |   k   
                                                          	       ]              0      E             
           d    @      x                      l          
                                                      $   k 4  
       @             \     h      t                           
     P  ]        $                                                 	                       4                                             5         5                 4           ComponentGroup: input p =  9 9 4  
          is not prime!  : 4        E   ComponentGroup: WARNING, don't know how to compute component group at   4  
        $  (  ,  0      4           A  2 2 4           p   d3 	4           phi ",p;  
4           mH    4           mX  \ X 4           ans  x 4                4           @    D     L        <  X          H    4           TamagawaNumber 	H	H	ʸ4  \                                       <   "    $   $    H   #  X   !               t   	           
                                !      #     "    	        	    	          h           <      0           	       0                         4  
                H          4           N has no square free divisors.   4     P  T      4           A    4           x !} 		4                4           d     h     l        `            H    4  
         TamagawaNumber 	`	4                                         0    x @          L     \          h                  	     x     $   $                                                                    	         d                H      T               <                            <   x                    
                           	             	                  ,                  4               4     p  t  x  |      4           A    4           p    4           cp 	    ,˸4           w    $  4                !4             t                            H    "4           Sha   #4                                        0     @                            P                $   \                                        	                                       H  	         ,       8                                p      |                  	            d                         !              '     $            (                                      8              T    L  	 l       ,         5       )      + 	   (                           0          <                           t         ]           	   @   h                                            
                                      4       @     L  !   X  $  h         t  *    '                                      $                                    )    (                	                              d                                             "     $    #                            t  ]       L      X       <            	     0                  $4  
                          %4        ,   There is no Sha associated to noncuspidal A.  ̱ &4                         '4           A   x (4           fac   )4           sha Factoriz*4           f  m l +4  
         S urn 0 ; en        ,4           p  {  -4           T = &*[Integ.4           f  8(  /4                04             @                               H    14  
         Eigenvector l[ h[ 24  4                                       0    ^          p    $         `                 T                           	                    34             44           T sic;      54           f  4 | 64                74             @                  d          H    84  
         Eigenvector (T,f);  94  L                                     0   	 y    	         	 $          `   
   l   
   x   
     
        
         
 T                    ,          l                                       (     4     @     P            	               \                                                                                                   D     P      \     x                          8                                  D                                     (      4                  	   	   d    t                                                     X  
              y                                   
  H   
   T      `    p         |  %      '    $           	     +     *             <  &                                                  @  	    L  	   X      d     t                 4                            /                                               (     4      @   u P               t          (                                     u                                                                  
   P     \    l         x               	 D                	           
                                                              H   	 
   T       `     p          |                       <            
      (       "	      "     "      	   `          #
 	    #               :4                                                                  c          ;4        <4        =4                                  <                    >4       ?4        @4                                  T                    A4           x   $ B4       C4        D4                                  T                    E4           a  7 h7 F4          $  (  ,  0  4  8  <  @  D  H  L  P  T  X  \  `      G4           T    H4           f  P 0 I4           n extension J4           K  ` | K4           Kn  ظ  L4  
         R rn Kn![1];  | M4           x   $ N4           L  x6 d O4           a  7 h7 P4           b  :  Q4           c  d = R4           i   l S4           Ln  $_ _ T4           v  l \ U4  
         --temp--           V4           w    W4           vv  , < X4           i  P D Y4                Z4           p  l   t     x        l            H    [4  
         ZAlgDisc ˸ d \4                                         0   4   <   4  L   4     \   4        4         4 $            5 y    5         5       R     6          6! ,    6        6             7 
T  7           8    $  7&    0  7&     7'    H  7A    T  7D   `  7F  p  7E         7@               75      77     74         7(                  7;    <        7(             7'         7'      7$                  8           p  7$       <     7#        8!    8         7     	    7                    ]4                ^4  
   |                _4           gens ;   `4           f ens.  t  Ta4           n  0 < b4           V egree(f); c4  
         g  i in [0..n-1]]   d4           i     e4                f4             4                           H    g4           DiscriminantOf 	D	B	ʸh4                                        <   @    $   @   L   @      X   @  h   @         A    |          A     A        A	         A              B              B     B        B	         B               C      C            t  @ 0             d  E   L  E    p  E     E          F!    F         F'     F$         G    G            G
     G
                I       I3 ? $  I2    Q 4  I%        I      $  I        d  J6    p  J@ y   J?         J5               J)      J+     J(         J                  J0    X        J            J     D  J            J
     J
        8       F     D      E X  \          M     M        M       M     M      M     M         M 	    M                   i4                                                                 j4        '   A must be a new modular symbols factor. h k4           l4           A    \ m4           f `disc := 1n4           i     o4                p4             4                           H    q4           DiscriminantKf 		B	ʸr4                                         <   S    $   S   L   S      X   S  h   S         T    |          T     T        T	         T              U              U     U        U	         U               V      V              S 0             d  X   L  X    p  X     X          Y!    Y         Y'     Y$         Z    Z            Z
     Z
                \$     \&  $  \#      0  \)     \        \         `  ]<  p  ];       ]4      ],    
   ]        ]     T       ]
     ]
               Y     @    p  X X            `   $  `      <  `     H  `   0  `    T  `   d  `         ` 	    `               s4                                                                 t4        '   A must be a new modular symbols factor.  u4             v4           A    w4           a  D9 @9 x4                y4                                          H    z4           SignedSubspace 	o	k	ʸ{4                                     0   h
    <   h : L   h          h `         l   h   x   h! :    h         h             h $          i       i       i     i           j)      j+      j* s   j(    X    j        j          D  k   P  k  `  k    c p  k        |  k!     k        k 8          l     l 	   l    c   l          l!     l      H  l             m     m    ,  m    8  m     m        m          t  n   \  n      n      n     n        n h          o      o      o             o            o     o              i    $         @  q   L  q     q        t  r   \  r      r     r           s 	    s	       r h              u     u      u     u         v      v	            t  u             L  x   4  x    X  x   d  x     x    	    x @       y    y     y          z 	    z      z     z    
     {      {	            l  z             4  }     }    @  }     }           ~ 	    ~	 P      } (  \                                     	                                 y            q 4                  |4  .      M         5         5         5         M         5         5                  M         5                  5         M                   }4        7   No +1 subspace since we are working in the -1 quotient.  ~4        7   No -1 subspace since we are working in the +1 quotient.  4           SignedSubspace: invalid sign.  \ 4               4           A  , 4 4           sign  * 4           S  4 4 4           Aplus  8 4           Aminus  X= 4                4           $    (     <           H          H    4  
         Eigenvector < 4 4  0                                      <       $       H               d   	  p                                             	                 X                           	             0              <     $      H              d  	   p   	                                              	               X                        	         \   0           @     L   	 \                       l             	          3      5   2        #                   
     
            L   x            @     (          	     4       4                                 	               	          4      6   3        $     (         
     
     
            |               p     X          	     d        t  @                      4  (      5         ,         0         5         4         8         :         :         :         ;         ;         ;          4        3   Eigenvector: when working in +1 subspace there are    4        8   no -1 eigenvectors, so the computation can not continue.    4        3   Eigenvector: when working in -1 subspace there are  | p 4        8   no +1 eigenvectors, so the computation can not continue.  D @ 4     @  D      4           A sic;  8 4           sign   4                4           T  \  X     \  
      P            H    4  
         Eigenvector minus; 	4  p                                      <       $       H                p   #   X   %       $   d   '       &     "          |                                               ^          l            0   @                 \                P           &     (      '     *      )      ,     %                   	                       X                  H   ^              <          $  l                                                            @                       y 0      ,                      `   2          |                                            p                 T                    $          ,  &    8  *  H  )         %             p   	   |                	                               d               	                     )         D                           8       0                
   t          	                   4        9         5                   5                              9         9          4     `  d  h  l  p  t  x  |          4           A  D H 4           p  	H	4           T  X P 4           f   | 4           e    4           F  , $ 4           V    4           b  t p 4           B  X T 4           i  l d 4                4                                         H    4  
         HeckeImages   4  f                                    0   
     <    : L              `          l       x   $ 1    #    :                           $                                     "      / 1   .         !                             \     h     4             P                    t                                                              ,       	    8       D    T       d         p  !                                                            # 	   "              X           ,        8  " # H  !    T                       x         :                                                                    4           (            d              X             L            ,      /      2 N    +            t  &                                     l      l               D  
   ,      P       \           	     8                  4        1         1         1         1         1         1      c             1          4  
                 4           i sic; en;  4           n    4           M    4           i  Ȅ Ą 4           p .. { { 4           s  l Xl 4  
         --temp--    s     4                4             l                               H    4           Dot c; mages4  r                                       0    y @          L    y \                    $                ) y    (                                                                                                   |        p         <  )    
         T           
 	                   4                 4           v   ` 4           w  ğ  4           i  + + 4           ans gree(v) 4                4             4                           H    4           DimensionAbelianVariety ] 4  X                                       <       $       H    k X          d                  * 1    )         !      !         #        / 1    .         2     1         #         #      t                    	     0                   4  
      5                     4       4           A sic; i]*w[4                4              @                   X  \      H    4           RecursivelyCompute_an  | 4  t                                     0            T        $                 t                       h                                                   y                          (   9 8          	       T                H                                                         ,     	                                  
      L    	   X  "  h         t  & 	     ( 
     +     -    ,       )       %                " 	     &     !    	     )      ,   $  .  4  -     D  *     T  (       `  ) 	   l  + 
   x  .     0    /       ,       (       1                  @                                (     4  "   @  %  P  !                                  "             1      3      5    4       0        $          t       l  	 x    `     (  	    4      @      L    \                                       d                               4              4       4        4                                  T                    4           q    4     $  (  ,  0  4  8  <  @  D  H  L  P  T  4           f sic;      4           start  h 4           eps   4           k   T 4           F    4           Q  D 4 4           q    4           n    4           fac ( d 4           p p)p^{k-1} 4           r    4  
         coef  := fac[1][2]; 4           m lse  // a_4                4                4           h  0   l             d            H    4  
         qEigenformTheta n;  4  V                                                    $       T     d              x             "     !                       H           @                            @          2 j    1     0  '     @                                T                               	     x          `              x                   p                        (  4 x 8  3        -       T  :   `  <  p  ;      |  B     ?                           
 H                           
  8                       `                D      P            	     8                                                                                   l  (      4  $     &    @  % y P  #       \  /  l  ,                        	      		      		                                                   ,  
                       h  
         L      X                @           #   |  %      $     '      &     "                                        \          P     	   	   @   ^             4  
   
   p                                               &     (      ' 	    *      )      ,     %      |        	  8  	    D      P    `         l  " \                ,        	      ^                
        d    R    $    	     - b   ,    L            
      
  8      D     P   	   \     l        x               
 ,                                  	  
                	  # y 	  "    ,          	  
         @	   2          \	      h	     t	      	     	                      P	                 4	  	              	      
 	       
  $    
  (  (
  '         #             P
      \
    l
         x
      
    
                        D
                  
  
    
         
  )          $  
 
                        D       P     `          l                 !	      !     !     |              8         $      $$ y   $#    L    $      ,  $
           %    %     @  %          %          `  %   l  %     %        % T         %      %  |  %                   &    &            &    &              '       '      '             H  '/ 9    '.          '      ' <  X             '      d       '               (	     (       (
    (
          (
             (
  ,  (
             (
  \  (
              P  (
      (
     (
 D    x  (
      (      (    (         (     (      (     (!      (&      ()    (%        (!        (!  $  (       0  (.  @  (-     P  (       \  (1    h  (3  x  (2        (0       (     l           '
              +     +       +    +          +             +  4  +            +  d  +        (     X  +      +     + L      +     +%       +2 j   +1          += @   +<          +A   t  +    +            0               $  .
     .       . 	    .               4  F      p         t         8         8         x         5         5                   5                                                  8         8         8      c                        8         8      c             8          4        "   Warning: theta series not be used.    4        "   Warning: theta series not be used.  D  4        '   qEigenformTheta: Computing q-expansion.  4       4        4                                  T        |            4           q  x9 9 4                                                           4  
         A for if if ,  4           prec   4           fac \  4           t Factorizat4           x    4           XJ  X d 4           V  ȫ ̫ 4           dummy GroupV4           p   h 4           T tors.  4           f  D  4           Mn  $  4           eig `6 d6 4           F   & 4           S  l* t* 4           b  D# L# 4           B  ! , 4           i  * l 4           e  &  4           i ]; O	ʸ4           MnF ile;   4           Q  |  4           q  x9 9 4           n xp := q; S4           p   @ @ 4  
         --temp--        | 4  
         --temp--        | 4                 5             L                               H    5  
      
   qEigenform    5                                         0   3   <   3     3     	    3 $                   5       5           A sic; p;  5                5              t   $  !   H                    H    5  
      
   qEigenform m(A,7); m5  j                                      0   9  @   9        9          :      : P               9 $   \             <      <     <        <      D  <              =      =       =    =         = p  ,      8  =$      =&    D  =% y T  =#       `  =/  p  =,         =               >	      ?	      ?	            ,  >               A    A        A	          B(    B'          B+     B     P  B            B
     B
        D      t  D     D          E       E1    E0       E;     ED 	   EC       E4         E4             E         E          ,  G     G         G	         t  D	 h    <       K      K h          L      L    L         L     L        M      M     M               D  L	           P      Q      Q               P	   ,         h  S      S        S&   t  S(      S'    S        S \          U(     U,    U+       U'       U        U          U
          8  U   D  U     U        U ,       t  U
      U
  T  U
     h              W     W      W 	    W       W   |  W           Z     Z    Z    ( $  Z    
  0  Z     Z      L  ]+    X  ],  h  ]+      t  ].      ]/      ]3    ]2        ].        ].      ^/      ^3    ^2       ^.        ^'    i    ]      $  ]     @   8  ]        L  ]    	      ]    
      l  _   x  _     _        _ `      `      `      `#    `"       `        `& 	     `'     `&         `&      `        0  b    <  b    H  b  X  b        b         b $       p  Z	     h        f     f      f     f         g     g            h   	  h           j     j 	       4	  k    @	  k  P	  k         k                l   
  l l	       	  m    	  m# y 	  m"         m             	  n    	  n    	  n  
  n       
  n#     n       ,
  o    8
  o    D
  o#    P
  o&  `
  o"       l
  o+    x
  o/  
  o.        o)        o      
             n 	  
       4  m    	  
    
  r    
  r      r      r  $  r        r       r     
              s   h  t    t  t.       t0      t \      s P             v     v         v         k    (	  x	      x       x  <  x                0  y       y    y     $            d  z    z        {      {     {     t            z X              }    }            }     }                         (   y          X     
   
            L        x   9                                                l                      "      ! y                           T     <           t       H   x                                                                           &      (    $  '    0  -  @  %       L  0    X  2  h  1        /                             `              	           " m          X                         ,  $  <  #                               X                 y                                                    #                  $      0  #    <  &  L  "       X  +    d  /  t  .        )                                          x                 (                                    <                           |       P                   p               D                     !      #    "             \                  4                 (               d      f	     8              "       !    !                            !            !  0  !             $             !     L      |  '     p     X           d                     "      !     $      #      .     2    1        -      @  	                   A   0  P      =              t  
    \          	     h              	5  f      (         8         8         ,         8         0         5         <         5               %   o                                8         D         8         8         8         8         8      c             8         8         8      c             8         8      c             5                  5         3          8      
5        ;   I haven't yet programmed q-expansions of Eisenstein series.   5        "   qEigenform: Computing eigenvector.    5        #   qEigenform: Computing Hecke images.   5     @  5        5                                  T        4  8          5           q  H @ 5           a_%o	----->%10o
 perverbose 5     L  P  T  X  \  `  d  h  l  p  t  x  |                            5           A  p l 5           prec        5           eig IsCuspid5           i / find i s5           Tpei if; Sup5           Q pei := Hec5           q  H @ 5           F    5           gcd Type(eig5           c then     5           d  D @ 5  
         one_over     5  
      
   startrecur igned A`q 5           f   startrec!5           p   // Recor"5  
         j   p := 2; time.  #5           coef  @ $5           m or|rt  %5  
         i   end while;  n &5  
         --temp--    s     '5           j  TZ PZ (5  
         m      coef := 0;  )5  
         --temp--    s     *5  
         --temp--    s     +5                ,5             h                            H    -5  
         Saturate  ؟  .5                                        0      <      H     X                 L   $                           "     !           &      (     '        %    /            +       2 6    -      0  +      <  + X             |         l  ' c |  &    2              P                                   `                                   (         4       	      P   R  `  !        l  %   x  '    &       $          +     -    ,       *    /           0      1     0         0       D       4  !    @  "    L  &  \  %        h  *   t  ,    +       )    /   !        /      6 6   1        /        / X              (       @            0   p         	     $              /5                                      05  
                   15           B    25           F    35  
         M rent(B[1][1]);  45           b  $c b 55           C  - ( 65           N   \ <\ 75                85             x                   0          H    95  
         SaturatePolySeq N); :5  h                                      0     @          L        	            	     \         $   h                                                  D                                          8                  ,               !    x   y                  l                 `                 m          H               @      1       4      0            H     X        d      p  $    |  &    #                            <             +                                             ;                           ,        t      \              t   h          F 2    E        0      3     5 	   4         /                          ,   	   8   
   D    T        d        p      |    
     #     %    $       !                                   * 
                    )             
                  ; 	     $       
       @  	     X                  ;5                                    <5       =5        >5                                  T                    ?5           q    @5                      $  (  ,  A5  
         P eturn t B);  `" B5           R rn P; en  C5           q    D5           f  Ԙ $4 E5  
         m  Parent(P[1]);  F5           f  | | G5           i  < < H5           X  Max([DegrI5  
         S ..m]] :  f in P]; J5           v  _ x` K5           i  pZ Z L5                M5           <  x   @     T        8            H    N5           IndexInSaturation    O5                                        0     @          L        	          	     \         $   h                                                  D                                          8                  ,               !    x   y                  l                 `                                          5      &       )      %             H      T                     <                    d                                       0                                  $     4          @  !  P          \  $   h  & 	 x  %    /           )      0 6   +        )         )                           T     	        	   (  ' a 8  &    	   D  0 b T  /     d                      	     7 
     9 
     ;    8        A     >    	      
      
                   
                 
            
               8        t                                    	            h                 
           	                   P5  
      L                     Q5     P  R5        S5                                  T        D  H          T5           q  P ( U5     X  \  `  d  h  l  p  t  x  |          V5           P sic; ntegeW5           R     X5           q  P ( Y5           f  8 H Z5           m    [5           f  T  \5           i   ` ]5           X  Min([Degr^5           D  X | _5           S ;  P];  `5           i    a5  
         ind hForm(D); ntegerb5                c5             l                           H    d5           EigenformInTermsOfIntegralBasis  e5  4                                      <       $       H                d                  X                                                                                  y          \           @      L   ,          \   4       |           $       *      -      )                                                     $          @             P                 p           9              0       +      .      *                	                                      % 	         L             \                      |             4    p  h                       
   
       >          4             '      ) ` $  &    P         T                           H       0   t             
             	                   f5        <                               <         <      g5                                 h5  
         A sic; , ind;  @ i5           B  h l j5           f  p t k5           F  qEigenforl5           d  `  m5           V  < H n5           n  D  o5           fvec ctorSpap5           g    q5           n    r5           Bvec  V![Coes5           W     t5                u5             L                               H    v5  
         qIntegralBasis   w5                                         0      <             	     $                   x5       y5           D  $9 (9 z5                {5                                            H    |5           qIntegralBasis 		u	ʸ}5  D                                          %    <   4     3       X   .    d   0     -          0   L                   $   t                  6                 	                        ~5            5           D  / @ 5           prec tegralB5           B  4% <% 5                5             L                                H    5  
         qIntegralBasis  ! 5                                         0      <             	     $                   5       5           A sic;      5                5           ,  8  0     X        (            H    5           qIntegralBasis 	x	u	ʸ5  h                                      <       $       H     X                x             l                          y              '     $                                          (                       H     T              p             d                                                       !     #                   <	           <   ( L        X              t                           h                                                    y          D           4                (        d  
#    p  
&   |  
(    
'         
"              	=      	G y   	F         	<              	      	     	       	- 	   (  	/  8  	,      H  	       T  	     `  	2     	         	                  	7 	     p       	              	                  
    X         	             	   
   
   0     <     H     X       h      ( x          (     %                        
                                   	                       
   @  #   (     P  "    2             4                    t          $    `       $    #               H                               	          <   
              0                  |  -      7 y   6         ,                                                              (  !    4  #  D  "                                    '    p  T             p  )                                   d                   $	                           	       	 0          `	  (  p	  '       |	  +           	   T	         	    	      x          
   	        	     	    
               ,
       	   
  
          L
     X
                @
       
  
      
  h
  
     |
            
  4 x 
  3       
  ;  
  7        -                       ,                        
                  
  <        E     @    p  X             |      '                   
     
                     	          (              D             8      l   9  |   8          <      &             `        
      
                                     P      (   <  |         !   t   0             h  #
   P  #       # 	    # \                  5  <      H         H      c          %             H                 %             4         5                  @                    H         P         H      c             H      c             H      5        D   qIntegralBasis: choice of Z[zeta_n]-lattice may be not well-defined.  4 5     D  5        5                                  T        8  <          5           q    5     T  5        5                                  T        H  L          5           q  L D 5     \  `  d  h  l  p  t  x  |                      5           A  4 4 5           prec tegralB5  
         --temp--    <   L   5  
         f sNew(A) then A):  5           Q  := qEigen5           g  p h 5           n  H @ 5           R    5           j ] :    5           i  l h 5           B   R := Pre5           C ]-lattice 5           F    5           q    5           g    5           n    5           NN     5           f    5           d    5                5             x                            H    5  
      
   AddFactors  8 , 5  p                                       0   1 ? @   1        L   1     X   1$ 	 h   1"        1      t  1 $             2     2          2             2#     2"         2               3    3             3     3              5  \  5     0       5     5       P      2       <        7
 	    7               5                  K                    K          5           5           A sic;  asis5           B  x p 5  
         F > ModTupFld / l 5                5             l                            H    5           IntersectFactors   | 5                                         0   ? ? @   ?       L   ?* ? \   ?)        ?         ? $          @ ?    @           @        @'     @"        @        @ |             A     A          A   0        A#  0  A"         A               B  p  B     D       B     B       d       D    D            D     D             A    P          F
 	    F               5                  n                    n          5           cusp y  y  5           5  
         A sic; := false;  5           B    5           F    5                5              X                  4          H    5  
         DualSubspace ;   5                                        0   W   <   W   H   W     W         W $         x   X      X      X     X         X l      =     Y         Y             Z       [       [#      [%      [               Z             D  ]     P  ],    \  ]. I l  ]+    X |  ]        ]        ] 8          ^ c    ^        ^            _      ` =   `         `      `              _             @  b    L  b    X  b$   d  b/  t  b#       b     	    b 4                  5                                5           Computing Ker(Transpose(f(T_ r Tr 5           ))) q xq 5  
      	    seconds.  f f 5  
          $  (  ,  0  5           M  ~ ~ 5  
      
   polyprimes  8} 4} 5           p  Xz Tz 5           f  w w 5           t  Hu @u 5           T ing Ker(Tr5           W r(M,p))); 5                5           @  @  D     \  
      <            H    5  
         DualSubspace 		5                                       0   l    <   l  L   l         l                m	       n	       n+ 1    n*         n	 t               m h                p       p      p     p      H  p	             q    ,  q   8  q     q      l  q	      =     r        r	 \           s	     t	      t)      t+      t	              s               v      v      v W    v      P  v	         4  w    @  w     w        w	 (        p  x    |  x e    x        x	 d  	         y	      z =   z         z      z            ,  y              | 	     |     |         |	         l    $            ~   p      |  ( 1    '          d             ~ X              
 	                   5        H         L         P         T         X      5           Current dimension =  R R 5           Computing Ker(Transpose(f(T_ G xG 5           ))) tF lF 5  
      	    seconds.  9 9 5           Current dimension =  { خ 5     `  d  h  l  p  t  x  |          5           M  |] t] 5           W  \ \ 5  
      
   polyprimes  tZ pZ 5           i  V V 5           p  HP @P 5           f  M M 5           t  J J 5           T  E E 5           fT  A A 5           K  > > 5                5                                        H    5           RationalPeriodMapping 	ʸrn (W); 5                                         <       $       H                d    ?              X            ! A                / 1    .    ,          h                      # " 0            ? 2    >      4      @            X  . 2    -       t                           h             #    L                                         (             4          L                  0                                   |       0   t             
             	                       5        T                    T         T          5               5           A   h 5           M  0 H 5  
         V  ModSymParent(A); 5           m      5           a    5                5                      
                  H    5           SignedRationalPeriodMapping h. `. 5  r                                      <       $       H                d    ?              X                   !                                !          H              & A   %       (  4 1 8  3    ,                      h      t   "            H 2    G                 <        3 2    2         !      #                                 (          X         $    h                                   =      t                     0                  " ,           I 2    H      0      <           T  3 2    2       p  ! 	   |  #                    d             ( 	   H                                         $             >          H             d    0                             \                           0   t                                              (            	           `     H      l     x            	     T          8                5        W                               W         W         W          5                             5  
         A sic; PeriodMap;  5           sign c b 5           M  ] d] 5           Bplus = ModS5           Bminus    5           V us := Sign5           m           5           b   P 5           m  | \ 5           b  8 h 5                5                                         H    5           RationalPeriodLattice 	ʸ 6                                         <       $       H                d   "    !      <  	 X             1 ?    0    g    #    2                                                                                 l  	          \  * U    )            P                           0   t             
             	                   6        U         U         U      6                 6           A  ; ; 6           pi    6           v  (U <U 6           B = Rational6                6           (  p  ,     0        $  T          H    	6           RationalPeriodConjugation    \ 
6                                         <       $       H                d   $    #          X             $    #                       2                          * ?   )    s                          7          L  "    X  % h  #       t  )    (       @            `                  4             2    (                                  $    ,   P                                      <             X  6          8   p         &       1 A   0         6    5    L   &        8      9   ,  8         8  X                           L       0   t             
             	                       6        V                    V         V          6     4  8  <  @  D  H  L  P      6  
         A sic; PeriodLat;  6           pi    6           Z    6           B   \ 6           star  Basis(6           b  <
 @
 6           C  := StarIn6           x  l h 6                6           `  T   d     p        \            H    6           ImaginaryTamagawa  P T 6                                                         0               $   <                 l                           ?          H                k                            	   8  	                	    	 ,    |                l  %    $         `                           ) b   (    L           -      /     -         -             8      D  (   P  . 	 `  -    c p  '    1              J    I       1                    ,                        0   x              $  
             	                   6        h         B         l                    B         B          6        7   (Warning: Imaginary comp group formula not yet proved.)  6        M   WARNING: Working in + or - quotient, so can not compute imaginary components.   6     t  x  |        6  
         A sic; PeriodConj;  6           M  p | 6           C if; n 1; W 6           Cmod2 ionalP!6                "6                                        H    #6  
         RealTamagawa   $6                                         <       $       H                d    ?              X             k                            	      	                _ 	    X      4                 $  %    $                T     `    p         |  ) b   (    L           -      /     -         -   t   H               $     *    )    c (  #    1 8          D  F  T  E     d  -                                               0   t             
             	                   %6        A                             A         A      &6        H   WARNING: Working in + or - quotient, so can not compute real components.    '6                 (6           A sic; so ca)6           M  T  *6           C if; ING: W+6           Cmod2 ionalP,6                -6                                         H    .6  
         DefaultPrec &  /6                                     2  0       <      L         X        d   *  t   )    
     1     -    E                       	          h   $                                     (            4   y D      m                           T                        <                            
 	                   06                   8         8                   16        +   (Using at least %o terms of q-expansions.)
 T7 \7 26             36           A  |  46           prec ultPrec56                66                                            H    76           Int1  ; 8 86                                      0   
    <   
 L   
     \   
	       h   
   t   
 #    
        
          
     
        
 $          
                                  # $       4         @       L    \      l                                                                                           ,         8  !    D  $   P  & 	 `  %     p  "     H           D      F    E        H 	   G         K      C                :      .                  >          X  .          ,  7     h  ,        )         
                      |  x      
         )                	                    96  
                  :6           alp /  : ;6           m  X; `; <6           n  ; ; =6           C  T< \< >6           c  < < ?6           s  t p @6           i  P H A6                B6             4                  0          H    C6           Int2 rn h D6  v                                                $        T   :     `   D y p   C         9                                                                                ,      .  $  +      4        @                                   4    H   P             l  )    
     	                   E6                F6          $  (  ,  G6           f ///   H6           alp   I6           m   | J6           C    K6           n  H D L6                M6           <     @     D        8  P          H    N6  
         PeriodIntegral    -sO6  6                                       0       <   ) R  L   3     \   )      h   6   t   7      6         6       9         	     $                   P6                Q6     H  L      R6           f  8 0 S6           alpha   T6                U6           \  4   `     d        X  |          H    V6  
         PeriodIntegral   W6                                         &        & $         T   (    `   (! y p   (          (                (3       (5     (2          (;     (8           '       '       '       '     '         '    (  '   4  '     @  '-    L  '/  \  ',      l  '       x  '      '         '                  (    H         '         )    '
     	    '               X6                Y6     h  l  p  t  x  Z6           f sic; dInte[6           P  (   \6           alpha   ]6           C  $  ^6           m    _6                `6             P                            H    a6           FastPeriodIntegral  ܼ Լ b6  z                                   R  4   6%      @   6(     6     d   6
     $      6             6      6     6         6 x            6      6     6        6            6       6     6                  0  7    <  7    H  7$    T  7$   `  7%   l  7&   |  7%        7%      7)     7#             7     	    7 $              c6  
                           d6             e6        f6                                  T                    g6  
         X m)  -> FldPrElt  h6           Y     i6  
                   j6           A sic; : m ik6           f    l6           g    m6           R f, \{oo, gn6  
         X m)  -> FldPrElt  o6           Y     p6                q6             @                   x          H    r6           FastPeriodIntegral  h \ s6                                        0   =     =      l   = $      \   ? $    ?         ?     P       ?          ?             @      @     @          @     @          A 	    A      $  @              ,  C   8  C  H  C       T  C     C       p  D   |  D     D       D     d   8  D             D    D            D    D              D       D  |  D     ,  D     D    D                  `  D   l  D     D       D     T   (  D             D    D            D     D              D      D  l  D       D     D    D                 P  D    \  D"     D!       D!     D     D!             D!    D!            D"    D!              D!      D!  \  D!       D!     D)    D%                  @  D-   L  D/     D.     p  D.     4     D.             D.    D.            D/    D.              D.      D.     D.       D.     D6    D2                X  C             H  G     G      P  G <  	   	   x  H 	     H "   H         H     H    H    	     H      H" #   H!       H          H$     H&    H%    	   (  H)   4  H+ # D  H*     T  H(    	 d  H#       p  H.   |  H0    H/    	     H3     H5 #   H4       H2         H7     H9    H8    	     H<     H> #   H=     $  H;    	 4  H6         H  0        l  H l  
      |  I 
   d  I     I         I     I    I         I     I    I       I         I     I!    I           I$   ,  I&  <  I%     L  I#     \  I        I        I p          J
      J     J        J       M       M        D	  M            M   	  M     M      |	  M        8	  M      M  	  M     ,	            l	  O x    O      	  O `	         	  P @    P      	  P 	         	  Q    Q      
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  R        R      P
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  S       S      
  S 0
        p
  T   |
  T     T      
  T d
        
  U   
  U     U         U 
        
  V   
  V    V         V     V      \  V 
        @  W   L  W     W        W 4        |  X     X     X        \      \$ y   \#         \               Z
     Z    Z       Z      Z  ,  Z       8  Z  H  Z       T  Z  d  Z    t  Z       Z       [      [    [         [    [         [      [    [        [      [        [,    (  [.  8  [-       D  [1  T  [0       `  [3  p  [2       |  [5    [4         [7    [6      [+         [:     [@      [B    [A         [E    [D         [G  $  [F       0  [I  @  [H       L  [K  \  [J    l  [?     |  [;       [9       [&    	    [         Y                  \             Y           0  Y	          ^5    (  ^? y 8  ^>         ^4             `  ^    l  ^  |  ^         ^"    ^!         ^'      ^*    ^)        ^%         ^     T             ^/             ^         )    ^     	    ^   	   L  d 	   X  d " h  d    	   t  d     d #   d         d"    d!    	     d$     d& #   d%       d#         d  0          d	 @        ,  e      e   <  e       H  e   T  e   d  e      p  e    |  e      e"    e!        e$    e#        e        e    e        e      $  e	       R    g&        g     8  g          g          X  g   d  g     g        g L         g      g  t  g             	     h      h "   h         h     h      h  0        T  h         D  i    ,  i      i        i 8          j    h  j      j        j t          k      k"      k$      k&    k%       k#          k*      k,    k+    ,  k       8  l    D  l$    P  l&  `  l%       l  l*    x  l,    l+         l.      l1      l3    l2       l/    	   l-      l    	   l         m      m"  $  m!       0  m*    <  m,  L  m+       X  m.    d  m1    p  m3    m2       m/    	   m-      m    	    m        k            n 	    n        X p                   t6     c          c          c          c                                       u6       v6        w6                                  T                    x6           i  k k y6       z6        {6                                  T                    |6           z   h) }6  $                           $  (  ,  0  4  8  <  @  D  H  L  P  T  X  \  `  d  h  l  p  t      ~6           A   ܪ 6           f FastPeriod6           Pg  ;  X 6           P IsNew(A); 6           g  @ 8 6  
         --temp--            6  
         --temp--            6  
         --temp--            6  
         --temp--            6           R  ؎ Ў 6  
         phi arent(P);    6           giP 0x 4x 6           C giP eq P; 6           i  k k 6           N  i  i 6           k  f f 6           e  Pd Hd 6           rootN  a 6  
         PI Sqrt(Level(A));  6           a  [ [ 6           b  Y Y 6           c  W W 6           d  T T 6           n   0 6           cn a simpler6           n  8 x 6           W 	=	ʸ6           WP  3 3 6           S = W(P)/N^(6           z   h) 6           ev  - ( 6           ans [ ,\ 6                6                                          H    6           SlowPeriodIntegral  0  6  \                                      0    j @        P                            `                $   l              $                                 T                               (                  	     8          D         x                l                 "                                    " #   !     $         0  $   <  &  L  %       X  )   d  + # t  *       (    	   #         .     0    /         3     5 #   4       2          7     9    8       (  <   4  > # D  =     T  ;    	 d  6           0                                                                                  (     4  !  D          P  $   \  &  l  %     |  #                                                <                               \	     	     0                 $           d     p                                                      p      
   
                        H              <             0  
  d                X                                       `                                 8              ,                  T                H                    "     !       !     |   P  !             !    !            "  (  !              !      !    !     D  !     )    %     8            x  -     /     .       .     l   @	  .             .    .            /  	  .            	  .      .     .  	    4	  .     6    2     (	            
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        (      4     @    P                                                                                                                   P       $                  D     t              h              0                                                               @                p         4     d              X                                  d  	 t                                            ,        8  !            T     `                   H   H                                                                            (    8      k                            	   p            !              %     '    &       $    i                 x     	              @                            4        $
    `           X       
        	                   6              c          c   	       c   
       c                     c          c          c          6        $      6        6                                  T                    6           X   $ 6           Y  Ա  6     ,  0  4  8  <  @  D  H  L  P  T  X  \  `  d  h      6           N sic; dInte6           k  x ܭ 6           P  4 < 6           g   4 6           fast   6           R   \ 6           X   $ 6           Y  Ա  6           --temp--    [             6           --temp--    [             6           --temp--    [             6  
         d while;  1;   6           --temp--    [             6           --temp--    [             6           --temp--    [             6           --temp--    [             6                6           x     |             t             H    6           PeriodGenerators 	@	ʸ-g[3]); 6                                        0     @              T   p       `   "  p   !                       $                                         ?            	              x          D  	           4   @          t  	 (         d  "    !        	 X                    D  	                                                       8                    d  	                	 X               	 x  	         + A   *        .                           
   
     	     	     	      \  	      
   @     L                4     
  |                  p                                          `  	                    T                   H                  	 <           s             t              8  
            1            & 1   %                     $      0       <  "    T  $                  x       H     	                      &    @        $     &    %         )     +    *      X  #             d             L          $                 Z    %                                       	                        x           $      0      <    L       h                          \                	                 $                5                             x	           <   1 L         X  ' 1 h  &      t  , 	   *            	                      &      	             <	         &        	      	       	                   d	         &                   X	       	  	 0          	  	                	           	    	       	  !  	         
  &  
  #    	 $
                         4
                	        
   d
             
  ( 
  
  +     '     	     
          
   
                     
               X
  p
  
       	 	  @
        X     d          x       L                   l                                         4                   
                (               	                       6  6      R                    l         l                                                                                           R         S         R         S      6         ! dR6        6                                  T                    6           a  @ 8 6           b    6        6        6                                  <                    6       6        6                                  (                    6                6        6                                  <                    6        $   WARNING: Not finding enough symbols!  d 6           Switching to slow method.    6        (   Could not find enough invariant symbols.  | x 6           Need a better algorithm.    6                                                6           A    6           fast   6           M    6           N   | 6           k  D @ 6           pi  Weight(A6  
         V > Mk/Ker(Phi)  6           S    6           G    6           X  L H 6  
         RR  []; V | V!0>; Ma6           a  @ 8 6           b     7           P    7           g    7           star   7           cnt 8	ʸ7           x    7           plus  H 7           minus  < 7           SS  $   7                	7           ,  h           0        (  8          H    
7           PeriodMapping 	 G	=	ʸ7  $                                       <        H   '    0      X   &    !        	     $               7     4  7           A    7                7           D  (          H        @  X          H    7           ApplyPeriodMapping 	`?	ʸec(A)); 7  T                                     0   !    <   + y L   *                       t                                                            h                  $                    )    
     	                    7     L  P  T  7           Phi v v 7           v  t t 7           i  pn ln 7                7           d  t   h       (      `  H          H    7  
         PeriodMapping 	xT	7                                        0     @                            P            d   $   \                                                                         $    !                      4   @            	 (        d  '   p  ' 
   '         '    '          '           '5 j   '4       '*         '           ,  ' X           )#      )&     )"      @  )        T  )          )	           t  *      *     *        *	 h         +       +        0  +            +     +     +        +        $  +      +    +                X  ,     d  ,2  t  ,1    ,    ,        ,	 L          -	       -          -      -              .	      .	            H  -               1	       2H   8  2    D  2     2   \  29    h  2=  x  2<         28                2'      2) 
     2+    2*    	     2.    2&         2                  23 
   P      4  2            D  2         2      2     ,             2C 	      P       2       l       2            4H     4      4     4     49      4=    4<         48              4  4'    @  4)    L  4+  \  4*       h  4. "   4&         4     (             43      x      4             4         4      4                  4C             4               4        |  1     4      l  7 ?    7        7 `          8 s    8      
  8            ;       :)      :-     :/    :.         ::     :<   $  :?  4  :;       @  :B   L  :D   X  :G  h  :C        :9               :2             :2      :2     :2     :,          Z   :(     	   9*    	  9    	  9     	  9  0	  9    	 @	  9       L	  9     X	  9"    d	  9$  t	  9#     	  9!      	  9            
   9*      9                  ;      	    	  9       	  6    9        9 	           >D   8
  =   D
  =    P
  =   
  =    h
  =1 P    =0       
  =" #   =!         =     x
             =%    \
  
    
  =       
    
  =         =    =        >    (  >  8  >    	  D  >    P  >     >    h  >8 P    >7         >) $   >(         >     x             >,    \        >             >         >    >         =                =     ,
             >?     
  ,    |  =       H  6    =        = `           @"    @!      T  @	            A      A      A      A         A                  A             A              A	 8        t  B! >    B       d  B	 h          G  2    G         F,      F2      F/     F1    `   F+     	   E5     E)      E-  ,  E,         E(             T  E    `  E  p  E       |  E      E    E        E         E     H             E#            E         )   E
     
   E5      E                  G             E       0     D     H  
     D    D        x        H    H            H  L  H              K       K A   K        K       K   0  K      <  K ( L  K      X  K!     K       t  L' g   L&    2    L"         L      L      L         L                  L    h         L             L        ,  M" R  <  M,       H  M0  X  M/       d  M< 1 t  M;    /   M"        M?      M@     M?        M? S    M        M              Q$ 2    Q#         P,     P/      P/   (  P0 !   4  P1   D  P0      P  P0 ` `  P+    " 	 D  O8   x  O, "     O0    O/         O+               O #     O    O    "     O #     O!     O         O         O                  O& #   l      `  O       ,  ) p  O    " 
   O8      O                  Q !     |       O            N            N
     N
               T	   4  T	               U     U	 (            X  V&  h  V%    2    V"    $     V    x  V      V         V                  V $   L         V             V            X     X           0  \$ 2    \#       L  [,   X  [/    d  [/   p  [0 %   |  [1     [0        [0 `   [+    & 	   Z8     Z, &     Z0    Z/         Z+               Z '     Z     Z    &   ,  Z '   8  Z!  H  Z         Z         Z                  Z& '     X      Z       t  )   Z    & 
   Z8      Z     @             \ %   $         Z          4  Y            Y
     Y
        (       K               D            `
   |  `       ` 	    `               7  F      l         X         Y         x                                                                       X         Y                 %                                   >                                      >         X          7        !   Not yet programmed for A not new.  ^ ^ 7     |  7        7                                  T        p  t          7           i  F F  7           PeriodMapping: Using WN trick.  > !7       "7        #7                                  (                    $7                %7        &7                                  <                    '7  
         fake lattice... 03 (7  
         NOT PROGRAMMED.  )7  ,                                                                   $  (  ,  0  4  8  <  @  D      *7           A  f f +7           n  e e ,7           k  lW dW -7  
         fast eight(A);  W .7           G  @N 8N /7           Q  J J 07           C  G G 17           i  F F 27           Cd  DD <D 37           x  4 4 47           i  8 8 57           P ast then p67           x  h* `* 77           i  0. $. 87  
         M ..#Q]] : x in G]; 97           star % % :7           x x[2][1],x[;7           v  X T <7           gens  StarIn=7           x  i  >7           z  ذ  ?7           z  X* l{ @7           periods of tA7           pi  P];  B7           g  (a | C7           PG  Lf  # D7           V     E7           b  c Pc F7           coord  * G7           i  ̔ # H7           b  ` < I7           S    J7           L  := [ pi(bK7           b  @ 8 L7           coord  \ M7           i    N7           b  H9 X8 O7           b   \ [ P7           coord  xW Q7           i   h R7                S7           T  h           X        P  `          H    T7  
         PeriodLattice    ` U7  $                                       <   e     H   e&    0   e   X   e%    %   e     	    e $               V7     \  W7           A    X7                Y7           l     p     t        h            H    Z7  
         PeriodLattice 	(	[7  X                                       <   k    $   k    H   k  X   k         k$    x          l   l   l       l       l'     l$         k$                m       m !   m         m         8  k 0              ,  o
     o       o 	    o                \7        >         Y         >      ]7     x  |    ^7           A    _7           n  @ < `7           dummy  p a7                b7             h                               H    c7        
   RealVolume a 	P	H	ʸd7  $                                       <   u     H   u#    0   u   X   u"    &   u     	    u $               e7       f7           A   X g7                h7                  
                       H    i7  
      
   RealVolume e		j7                                       0   |      | x   P       \   |   D   |    h   |  x   |         |              |(              |+      |-       |,       |C     |@         |(                }!    }       `  }           0  ~" ? @  ~!    g P  ~    2    ~        ~ $           0      &      $      %         #                  +    t        #         U   "    2          H            8  (    '         ,        h     t                # t          H   \           2                                                                             ,  	       h      t   !         <  
 \  
   	      9 
     *      . '  )    P                               4          ,           6                    \      h      t  "    !           	     (    '    L           *      +     *         *      P               t                 8  #  H  "       T  2  d  1        %            ,                                       #                          	            
  4  
          
             
  t  
     H       
    
        h       
      
     
       
       T                                 <  | $             0  
 	            	     $                  k7  "                ?         Y                    ?         ?         ?         ?      c             ?          l7                                   m7           A   T n7           n    o7           r    p7           B  D  q7           v  ܡ  r7           S  Basis(SkZs7           Conj sis(Vect7           P  Ĩ , u7           v    v7           Z ce.    w7           Phi ȵ , x7           z    y7           C := PeriodMz7           R  p t {7  
         --temp--    Ģ     |7                }7             h                                H    ~7           ImaginaryVolume X		ʸ7  $                                       <        H   (    0      X   '    (        	     $               7       7           A   3 7                7             T                 X          H    7  
         ImaginaryVolume P	7  n                                      <       $       H     X                 x          #   l   %       $       ;     8                          !           ,                " ?   !    g       2                         0    d  &    L  $      %         #     X             +    @  t      #         U   "    2                        (    '      l           4     @    	 P         \  # t             (           2                                                                          P     	       4      @   !           
 (  
   	      9 
   |  *      . '  )    P                  p             4    d                 6                    (      4      @  "  P  !     `      	   l  (  |  '    L           *      +     *         *                 (    '         7    6        *     <                           0       0                
   l          	     x              7        @         Y                    @         @      7        $  (  ,  0  4  8  <  @  D  H  L  P  T      7           A  $ $ 7           n  0& 8& 7           r    7           B  x1 |1 7           v  8 8 7           S  Basis(SkZ7           Conj sis(Vec7           P  > > 7           v  t l 7           Z ce.   ; 7           Phi d \ 7           z  
 
 7           C := PeriodM7           R    7                7           d  L           h        `            H    7           ellinv_NormalizePair   7                                        0   
    <                  $         l    $|                                           
                            
         t   `                
    (      4   #D      E T       d                               
                              ,                         B                     
    	      t     0          d       
         X                                              $      '     &      h  "            
          (   #8      E H       X                                                   	 |              @       
               	                       7     l  p  t  x  |  7  
         w1 ic; gvolume;  7           w2    7           tau  | 7           i w1/w2; *Ro7           w3 f; ; l 7                7             L                            H    7  
         ellinv_c4c6   7  $                                      0       <              l    $                   `                                                           H                                (   #8                            h      t                $                   \                              )         +      (  . # 8  -       D  4 *T  3     d  /    	 t                     	                                           
   
      
                T           8      D             t   ,                 h                
                                ,        
                                 p          L    X                        B                     
    	         t                             (  	           	                           P      \    l         x                                          D                                               T                  H                   <         0      @         
 B   	    
                                                                                       T  
   `      l    |      	                       8   H          
                                          (             d           X  
        	     L                  7     V                           7                         ܔ 7           term =   w 7        ,   ellinv_getc4c6: WARNING: precision very bad! u u 7                                                     7           w1 turn  7           w2     7           tau   7           zero   7           one p h 7           two   7           pi  п ̿ 7           x    7           y    7           q  two*pi*Im7           f n(x));  7           f2  ģ  7           f4   ؠ 7           term   7           qpower  | 7           sum4   7           sum6   7           tiny   7           n    7           n2    7  
         c4 m = ",term;  Pw 7           c6  o o 7                7             h                               H    7           EllipticInvariants 	{	ʸ7  $                                       <        H   +    0      X   *    +        	     $               7       7           A eturn  7                7              \           $  	        L          H    7           EllipticInvariants 	    ʸ7                                         0   "  @   !      L   (     %          $       x                  l                  " %         X               '      )      ,    (         0      2   ,  5  H  1                &      l       <                                           !                                               $      0    @         L    \         h    x           !      $    #         '    &         ,      /    .       *              p           $      0      <      H      T        
           	                   7     (  ,  0  4  8  <  @  D  H  7           A  8\ 4\ 7           n  Z Z 7           L  R R 7           tau    := Pe7           w1 rt } X 7           w2  O O 7           c4  I I 7           c6  H H 7           j  E E 7                7           X     \     d        T  l          H    7  
         AbelianVariety  L3 7  8                                       0     @         L   $     !                 \                $   h               ,        	                        7        `      7        $   Not yet programmed for dimension > 1 - H- 7     h  7           A sic; w2, c7                7           x  d   |  !           t  $          H    7  
         EllipticCurve e(A); 7                                        0                         @                $   L                                                 0    |                  @                                                             T    d                          t              H              	 j   	       	        	         
      
              	             4    D        P  $     !                `              (  l            $ ?   #    Q            	                              '     &      ,  *  <  )    E L        \        h      t  . m                                                       y          <              3      5 +,  2    $          P          d          x                                                                                                                 	  D     T        `      l   E |                         8     
                        E                        ,            !   L  !    	        "   l  "	 @  
        #     #	 `           $     $	            %     %	           &      &     &                & 0            T  &	            '      (      ( 0           $  ' $  <           *	      +	     ,      ,       ,      ,	   
     -     - 
   -         -     -         .      .               -	             + x         \  1    h  1  x  1       1!      1%    1$        1           ,   1       	  1 P         2      2    	  2      2            4  2       -        H	  3  X	  3        d	  3#  t	  3"        3         4   	  4 	           5   	  6    	  60       63      6 	    
  5	 	  	         
  8 .   8      x  8 	       8
  9    D
  9      9             l
  : 9 |
  :          : 
  
      
  :)  
  :(       
  :0 
 
  :,       
  :5  
  :2         :              ;!      ;'    ;&        ;       `  ; 
        P  <' /   <&      H  < D          =      =$      =&    =#        =          >     ?      ?'      ?)      ?            $  >              A   8  A      
    B         = t              : `
  0         9    ,
  `       F     F     F          G      H      H              G               J 	    J         F	           4  3 <	  	      
   X  N	 	   d  N     N          O      P      P            H  O	 t            R     R        R      R* y    R)    2    R/ 	   R-    E ,  R"      <  R         R     R          h  S9    t  S; +  S8    $    S%        S     \     S	          S          S          S        x  S             T   $  U       U   `  U            T  V       V      V H             T	   0          X     X        X      X# E   X"        X         X   d  X          Y      Y      ,  Y    8  Y# E H  Y"      X  Y         Y     Y            Z      Z     Z        Z x          [     [   
        \      \            ]      ]            ^      ^          N L           X  `    d  `    p  `     `              `         `      `    
    b	      b    b                  d      d     d          e   ,  e 	 <  e      H  e$ 
    e       x  e            f   L  f l          g     g     g         h     h          i      i     i                 j      j  <  j                 k         g             d   X            n    n     |   0  n            n      o     o         n      n    n       o      o     o                 @  n   L  p     p       h  n      n    n \      p      p     p                  n     q     q         n      n     n       q      q     q                H  n   T  r     r       p  n      n    n d      r      r     r                  n       n     n        r <  |         q            p 4  t       H  o         p  s   d  t      t     t     X             u      u      u     u              u         u&     u#         c	 d         ` L             * l  8              7  f                                                                                                                                                                                                                                                                                c          c          c          c          c          7        +   EllipticCurve: A must not be a +1 quotient. !   7        +   EllipticCurve: A must not be a -1 quotient.   7        %   EllipticCurve: A must be of weight 2.   7        "   EllipticCurve: A must be cuspidal.    7        E   EllipticCurve: A must be on Gamma_0(N), i.e., have trivial character.   7        9   EllipticCurve: A must have rational fourier coefficients.           7           c4 =  T+ 7           c6 = z  { 7  
         Searching... ` x` 7  
         [%o,%o]  ^ l^ L^ 7              Y | 7           Candidate curve [%o,%o]:
     7  
         Rejecting--the  keVe7        !   th L-series coefficients disagree    7        2   By Shimura-Taniyama, this is in the isogeny class.  ,X 0X 7        1   
Recomputing period integrals to higher precision  ^ t_ 7  
         c4 = nts(A,n));  7           c6 =   7                                                       7           A  8' 0' 7  
         sturm  h l     7           n = HeckeBou7           f m);  l 7           w1  D{ L 7           w2  k  k 7           c4  j k 7           c6  xh (h 7           j  l l 7  
         maxtries r p good an7           tries  & 7           rad  ) 7           cur * *  8           dir 0; 1000;8           seen ;   // 8           E if; f; Y 8           found   8           EE    8           p   ȸ 8           EFp  43 8           ap     EFp :8  
         --temp--    s     	8                
8           0  t           4        ,  @          H    8  
      	   LAnalytic d.  n };  8  (                                       0   ~    H   ~     T   ~$    <   ~   d   ~#    0   ~     	    ~ $                   8     8  <      8           A  H  8           j  ܴ @ 8                8           L  0   P             H            H    8  
      	   LAnalytic c(?	?	8                                            d          $       T    @             
 H            
                      :              x               
         X                                        L           ,       @        R    %        (            
     t   X                              ,                                       L                 @              1 ?   0                                        !      $     &    %         )      +  0  *     @  '     P  "     `         l  0               Z   #                
 t  	                !            
   
   
       	     % '         l  
        @      L   \       l         x       !                     .     0    /    1  -       #         4      8     :     9     0  6     @  2       L  ?  \  =    P            
 4                           	                       	                                  B                                     0             L  )                            	            d              - 2   ,      H  
              (    8                |  
       l  (               
     \                                 0                                                    `  
         P             	  
 D                                                                           t                    	  
  	       <	      H	     T	      `	     p	        |	   3         	  
 0	        	    	  
       	   y 	                $   	    
      
  !   
                        H
  ?    T
  C  d
  B         >            
      
     
      
       
  "  
  !      
        
      
  %       +     .    *     ,         8  2    D  4  T  3        1              
             9    <
  d               )                                   	                           D  
            
 	     8                  8        \         l                                                         8     `  8        8                                  T        T  X          8           i    8     p  t      8        8                                  T        d  h          8           X  x , 8           Y   @ 8             8         8                                  (        x  |          !8                "8        #8                                  <                    $8                %8        &8                                  <                    '8       (8        )8                                  T                    *8           a  \
 X
 +8                                                          ,8           A   | -8           j  L P .8           n   X /8           k **********08  
         C j le k-1; A);  18           i    28           R := Complex38           X  x , 48           Y   @ 58           x := Polynom68           Phi ]>);   78           z := PeriodM88           zz  % % 98           e rn 0;  :8           Q    ;8           PC  
 
 <8           a  \
 X
 =8           g  0 ( >8           P    ?8           f      @8           roots P!f : A8           j    B8           i    C8           Lfval    D8                E8             t                      ,          H    F8  
         ClassicalPeriod z	G8  (                                       0       H        T   ,    <       d   +    4        	     $                   H8     $  (      I8           A    J8           j  p h K8                L8           8  4   <     P        4  h          H    M8  
         ClassicalPeriod  	N8                                              H        $                 h      t              ,   \                                            1                          	        ,       <        H       T  % d  $     t  !         ,     . 	   -       *       (                             	              0          1     	                        O8        H      P8     L  Q8        R8                                  T        @  D          S8           i    T8     T  X  \  `  d  U8           A    V8           j  8 0 W8           n    X8           C {ioo\} f(zY8           i    Z8                [8           t  x           x        p            H    \8  
         is_approx_zero  is p]8  (                                       0    B @       
  L     X     h                	     $               ^8     |  _8           x    `8                a8             h                            H    b8           DerivG1  c8  Z                                      0     <                   	     L        $   X                                     5                                  
              X  
           	    <          >      	 0    |   $  H                 
 p                                 	                   ]          	                 d                   H      T                <         	                 x                                          
             	          <  
               	     0       	   d          K      	 X       L  p                	                	                  	              D  	          $    4                 	   	     d    N p                  
              
                              C          p               	   (    8         D      P    `      	                  	                          $     	                                          	          D                 d   8                  X     
                  C             x     	                         	          (        	         H                    <  	      h      t                	             \                                            4  	                $                        T      `    |        H                   	           	 p                              
 
   X      	                
   @	  
 	               
 	     4	              d8                       V         V         V                      e8        *   Computing DerivG1 for x = %o using series
  ( $ f8        7   Computing DeriveG1 for x = %o using continued fraction
 Ȏ g8  
                      h8                        | x i8  
                     L j8        ?   In function g1, continued fraction method, reached end of loop! N k8                                   l8           x  D @ m8           ans   n8           p    o8           ok %o using p8           n := 0; "Comq8           term   r8           a0    s8  
         b0      $   t8           b1      Ȋ u8           a1  0.0;  omv8  
         k = Exp(-x);   w8  
         ca  IsOdd(k) then   x8           a2  @| <| y8           b2  s s z8           newans  X {8                |8             h                             H    }8           DerivG2 TO ~8                                        0      <        	           	     L         $   X               5           
                                                                                      <  
    H    X        d    t         "             2      (       %        6    5    	             0          
             0    <                    d             
     X  ]                             
                                                 @          4             
     (           h       t              \   	                 ! 	    !	                         $  p       $     $                %
 	    %                   8  
                          8           Computing myg2 for x =   ? 8        $   In function g2, reached end of loop!  p 8               8           x  \K `K 8           ans D D 8  
         p ealField())/12;  8           n 1; *ans/2 8           term ) ) 8                8           ,  h   0     @        (  X          H    8           DerivG3   8                                        0   +   <   +     +	          , 	    , L        + $   X              . 5   .        .
          .     .        .            /       0        0       0             0  /            @  2    P  2      \  2  l  2      x  2      2!     2%    2$       2     	   2         2*    2(        2.    2-        23     2J     2I        21      P  2 0         3
     3 D       p  4  |  4      4              5       5    5         5     5     <  5
                   6      6     6  ,  6        6      h  6        \  7       7    7
     P             8      8    8        8	      8          9 	    9	        8             4    d         <   D  <                =
 	    = 8                  8        4      V   8         <      8           Computing myg3 for x =  | 8            ' ݙ	1V	`		8        $   In function g3, reached end of loop!     8     D  H  L  P  T  8           x    8           ans 8 4 8           p ans/12 - 18           n -1; RealFi8           term  -x/n; 8                8           d  0   h             `            H    8  
         DerivWt2   |  t  8                                          D   T   D       $        E   x   E       H         G     G     l    d  G             G      H     H          G       G     G         H      H            G   (  I     I       D  G      G  l  G 8       I      I `          G     J     J         G      G    G        J      J           G      G  $  G        K      K        J            I   P  4    |  H       L      L      M     M        M	          O"       O, y   O+         O!              O      O  (  O       4  O  D  O       P  O  l  O          O	      O         O     `             O      |       O             O            P      P"    P        P        P
         8  Q ( H  Q
      T  Q     Q     t  R+        R       R     d      R    	   	     R	     R	     R	      8  R	   
   	    R 	     R    R                (  S     S      h  S         X  T y    T        T L          U     U        U |     
    V 	     V     V      V     V        V 3   V      d  V         (  W  8  W       D  W y T  W        W        W       [      [    [         [              Z       Z y   Z         Z              Y 	     Y      Y     ,  Y#    8  Y%  H  Y"      X  Y      d  Y    p  Y(    Y'         Y*      Y0     Y3    Y/       Y         Y9      Y;    Y:        Y7         Y
                  Z          L  Y
         )    Y         X     0             [    t  \      X       x      X      x	  X
          \      \ 1  \      	  \    	  \   	  \     0	  \       <	  \) 1L	  \(       X	  \,  h	  \+        \        \
                	  ^    	  ^ 1	  ^     
  ^      	  _/     	  _9 y 	  _8         _.              
  _    (
  _  8
  _       D
  _  T
  _       `
  _"    l
  _$  |
  _#        _          _     
             _)    	  
    
  _       
  ) 
  _
        ^         ^
 	       4  Q ,    
        a
 	    a (                  8  (   c                   c                   c                   c             l      %             x                                8           r must be 1,2, or 3.     8     |  8        8                                  T        p  t          8           a   4  0  8                                           8           f sic;    8           N       8           r   h  d  8  
         --temp--    I     8           Gr  ,  $  8           rootN   T  8           n       8           G = Sqrt(N);8           Q   |  x  8           PC      8           a   4  0  8           g       8           d       8           P           8           roots = Prei8           j  T, ` 8           n  Dk Hk 8           ans t be squ8           n  ` ` 8                8             L                             H    8           ComputeSpecialValueAndRankWt2  $ 8                                        0   f    <   f     f      |   f $          l   g     g         g `             h    h        h             i     i     i          i    4        i    i       $  i  4  i         i             T  j   `  j    l  j 0|  j          j 	    j H      i               l     l     l         m      m     m 6   m        m         ,  n B <  n    
  H  n  T  n  d  n        n         o      o 	    o	 t      n                q	      r	      r      r      r	               q             l            8  u  D  u     u       `  v    l  v   x  v 6   v        v T          w B   w    
    w    w    w        w         x      x 	    x	     x  w               z	   H  {	    T  {      {      {	 <              z 0  `          u ,             ~     ~     ~                     6                    $   B 4      
  @    L    \                 x         	    	 l                     	           !      $                                0  ~                 `   $            T  
      	     H              8                                                                    8  
      
   L'(A,1) ~  se then  8        #    hence computing second derivative. d u 8  
         L''(A,1) ~  e then  8        #    hence computing second derivative. D, X+ 8           WARNING: L'''(A,1) ~   g 8            even looks zero!  Giving up.  n 8        $   WARNING: not able to determine rank. f e 8  
                   8           A sic;  Z 8           n    8 8           f    8           N    8           e  x H 8           a  p  8                8           (  t           ,        $  4          H    8           LeadingCoefficient 	  	ʸank.";  8  (                                       0      H        T   -    <   !   d   ,    .         	     $                   8     0  8  
         A eturn eturn   8                8           @  X           D        <  P          H    8           LeadingCoefficient 	    ʸ8                                          0      <       H   ! .         	     $               8     H  L      8           A  8= 8 8           n  i 2 8                8           \    `     h        X            H    8           LeadingCoefficient 	  	ʸ b ~ 8  ~                                       0    j @        P              d          p   ) @    (         /     ,                         /       1             .                                        ,      8       D  6  T  5     d      1t                   ; 	             $                	                                8        d      8           Not programmed for weight > 2  f 8     l  p  t  x  |  8           A    8           j   `" 8           n LeadingCoe8           Lval . s 8           r  g Tf 8                8             8                              H    8           mu0 ********8  X                                       0                        X   4     3      t                                       	                  h              !    L                    5 (          
     	     $               8             8           n l (l 8           t  =  8                8                                            H    8  
         mu20 zation(n)]);  8  l                                       0      <    
 L          X                   	     h        $   t              H     G              +       .      0     /    7  *    	                                5           x        4    L          
     	     h              8             8           n    8           t  D - 8                8                                            H    8  
         mu30 rn rn t# `$ 8                                         0      <    
 L   	       X     h                |           	      
              $     !                         	             $                H     G      0    <  +    H  .   T  0  d  /    7t  *    	                  $             5                                
     	                       8             8           n           8           t  f  8                8             8                           H    8  
         c0 turn rn r* * 8  X                                       0   @     ?       L       X   %   h   %      t   '        )       +     *         '         '         8                 @              2    $        (            )    
     	                   8                8             8           n  2  8           d  L x 8                8                                         H    8           g0 turn eger 9  |                                      0      @         L      d        p       X                           	               '      "      &         *     )       !          1      ,   (  0      4  4  D  3     `  +        l  9   T  6   |  8        <    ;       5                  	     $                   9                9       9           n  |l q 9                9             H        $          ,          H    9           mu1 ; gers()9  ^                                       0      <    :            d       L              	     X                                " 8   !           )       %      (        $        ,    +      ,            	              $   t   8              9                	9     (  
9           n  ,' 8' 9                9           8             <        4  D          H    9  
         mu21 eturn   ) 9  4                                       0      <                d       L              	     X         . 	    '          $   t                  9     @  9           n  ] ] 9                9           P             T        L  \          H    9           mu31  hen re9  4                                       0      <                d       L              	     X         . 	    '          $   t                  9     X  9  
         n urn 0; end if; ] 9                9           h     l     p        d  |          H    9           c1 n; hen re9                                         0      <    :            d       L              	     X         $   t                                   	          |                             4       ,  R     Q       H  " 8X  !      d  6   t  6        8       :      <    ;        8        8 8  -       $        @     ?              <             D            P           ) `        p            	                        9  
                             9     t  x      9  
         n urn 0; end if; Z 9           d    9                 9                                        H    !9  
         g1 turn rn  ^ ] "9  |                                      0      @         L      d        p       X                           	               '      "      &         *     )       !          1      ,   (  0      4  4  D  3     `  +        l  9   T  6   |  8        <    ;       5                  	     $                   #9                $9       %9           n     &9                '9                                            H    (9           ss0 ; gers())9  f                                      0    9 @              T          `       l     
 |             %     "                    p   $                                
                   $           4       D       T        `   	         	                    *9             +9           n   ( ,9           p  2  -9                .9                                            H    /9           muXNp n )  )09  ,                                       <       $   
   X          d      L      t                	     0                   19             29           n  ؟  39           p    49                59             0                               H    69           mu2XNp  \ 79                                           
 	     $               89             99           n  D ! :9           p  ` 4" ;9                <9             0                               H    =9           mu3XNp  l >9                                           
 	     $               ?9              @9           n  p% % A9           p  @ T B9                C9             h                     $          H    D9           cXNp ( |( E9  $                                     <   
     H       0      X                	     $               F9              G9           n   ) H9           p  t) ) I9                J9           0             4        ,  @          H    K9           gXNp  (n);  L9                                         0       <                  X       d               L              	     t     D    $               
                                           	 <          0  %    H  '   $     X  $      d  *  t  )                                                              %      '           $      $  *  4  )             	                        M9     8  <      N9           n  dc Dc O9           p  b b P9                Q9           L             P        H  \          H    R9           ss1 ; - mu3XS9  b                                      0    9 @              T          `       l     
 |             %     "                    `   $          	       	       	
      	        	       	      	   $  	     4  	     D  	      P  	  	    	     	    	                T9     T  X      U9           n 2 ;  \\ V9           p    W9                X9           h  @           l        d  t          H    Y9           eisen (n,p) Z9  4                                       0    9              $       \      h     x                              	     P                   [9     p  \9           p   X ]9                ^9             L                |            H    _9           S0 n; rator(`9                                        0   
    <                 $      h       t    :    	                             
                                            	             \             0     <               d      L             	     X       $  t                                                                      #  0  "     @         L     X  
  h  	      t                                     	   &                              #     %    $    C ,  "     <      	 X          d  -   L  (   t  ,         6     8    7    C   5       /    	   '                  	                   a9                b9             c9           n    d9           k    e9                f9             L                            H    g9           S1 n; *c0(n)h9  z                                      0   
    <              \   $      h       t    :    	          ,                                             !      ' 
    #         ,    )      ,                                 	      @       \   L           "     "     "          #      #            8  " t             %     %     %          &       &      &     	    &       %   (          \  (   h  (     (          )      )   x  )      )     	    )       ( P             +	     +    +
          +      +   $  +      0  +  @  +     P  +       \  +   h  +  x  +        +    +          +#     +      +"       +    	    +      X  +            ,     ,    ,          , ,  p     8  ,   D  , 
 T  ,       `  ,  p  ,         ,             -      -     -                   .     .     .
        /      /     /    /    C    /        /                  .   $          ,     @    |  1     1        1      1     1         1 	    1 p              i9                                  j9           S1, k = 1 not programmed.  |  k9           l9           n  < 0 m9           k    n9  
         a rn S0(n,k);   o9                p9                                           H    q9  
         idxG0 gers()!a; l{ r9  r                                       0   6D     6C       L   6   X   6  h   6       t   6      6     6        6          6!      6#     6"          6'      6)     6(         6,    6+       6%    	    6         6     @              61    $   ,      6      H    `  6        6     	    5 |                  s9             t9           n  $k  k u9           t   / v9                w9             x                               H    x9           idxG1 ers()|y9  (                                       0   : 8L   :        X   :    @   :   h   :        :     	    : $               z9       {9           n   4  |9                }9                     <          `          H    ~9           CompleteCyclotomicField ʸ9  >                                     0   M    <   M     M        X   N! 9   N      |   N     L       N             N      N     N        N            N       N     N                  O      p  O         0  P    <  P   H  P    T  P   d  P         P     P $          Q       Q 	    Q     ,  M $   h            S 9   S        S        T      TW      TY      T            `  S            P  V :   V        V D          W     W       W     t     W            W     W     W        W           W      W    W               4  X    @  X   L  X     X  X- ;h  X,      x  X        X    X        X1     X3     X0        X (          Y     Y      Y     Y               Y  0  Y          Y          P  Y   \  Y     Y        Y D         Y      Y  l  Y                  Z
       Z 	    Z                   9                                              $                    4      9       9        9                                  T                    9           zeta . - 9        H   CompleteCyclotomicField: the place v must be 0 or prime; however, it is  \ \ P\ 9           .  [ [ 9     (  9        9                                  T                     9           x    9     8  9        9                                  T        ,  0          9           zeta  L 9     @  D  H  L  P  T  X  \      9           p eturn )   9           v   ' 9           F    . 9           zeta . - 9           K  c Pc 9           R   @ 9           x    9           f  Polynomia9                9           cond     9           f          /9           pn aZ's.   9  
      	   istrivial   |    w                                                                                       $     (     ,     0     4     8     <     @     D     H     L     d     l     p     t     x     |                                                                                                 !                                                                                                                                            $     (     ,     0     4     8     <     @     D     H     L     P     T     X     \     `     d     h     l     p     t     X     `                                              H     \     `     d     h     l     p     t     x     |     4(     T*     \*     `*     d*     h*     l*     p*     t*     x*     |*     *     *     *     *     *     \1     d1     l1     p1     7     7     7     7      8     8     8     8     8     8     8  G   8      8     $8     (8     ,8     08     48     88     <8     @8     D8     H8     L8     P8     T8     X8     \8     C     C     C     C     C     C     C     C  	   C     C     C     C     C      F     F     F     F      F     $F     (F     ,F     0F     4F     8F     N     N     N     N     N     N     N     N     N     N     N     N     N     N     N     0T     @T     DT     HT     LT     PT     TT     XT     \T     `T     W     W     W     W      W     $W     (W     ,W     0W     4W     W     W     W     W     L\     P\     _     _     _     Xd     \d     `d     dd     hd     ld     pd     f     f     f     f     f     f     h     h     h     h     h     k     k     k     k     k      l     l     l     l     l     m     m      m     $m     (m     ,m     0m     4m     8m     <m     @m     p     p     <s     Ds  .   Hs     Ls     Ps     Ts     Xs     \s     `s  
   ds     hs     ls     ps     ts     xs     |s     s     s     s     s     s     s     s  	   s     s     s     s     s     s     s     s  
   s     s  ?   s     s     s     s     s     s     s     s     s     s     s     s     s     s     s      t     t     t     t     t     t  
   t     t      t     $t  	   (t     ,t     0t     4t     8t     <t     @t     Dt     Ht     Lt     Pt                    Ќ     Ԍ     ،     ܌                 
   t            	   |     d  	   4  	   X     x     |               d     h     l     p  	   t                                 9     H  L  P  T  X  9           eps c; td; r9           std 9 (9 9           R   : P: 9           h  ; ; 9           i  5 5 9           h  4  l     p  
      d            H    9           DirichletCharacter 	    ʸ9                                       0   &    <   :  L   9    1 \   2         %                                                                               x                   $                                  T  !   `  %  p  $                         H                                5                 4                 $                        T  "    `  &  p  %         !                                                                      H                    t     	       @   	   L       X  &    d  ) 7         	     4                  9                9     t  x  |                    9           N  `{ | 9           std  Й 9           p  ,| { 9           i    9           lift  T 9           e  U dU 9           d d))]];  9           r  h l 9           i   X W 9           pows div d; 9                9             |     /     +                H    9           DirichletCharacter 	    ʸ9  	                                        /     <      H                        X                0   d                         ,                       
                            
  $  	       0    @                         	 P                 \           
    	         	                                       	                                t        P  $  `  #    ?p      @            D                                  
                                            ,      8      D    T       d                                t                                   
                                    ,  !   H              T      `    p  
             d       ,      0    /         +                	                        !                                        & 	     0             L                       
                            	                   " 9   !     0             
          P     \             D   D         
      
  l  
                               0                                $                            	            h     t           R                                                                R           x          8      D     P     \     l                  ,           \        ,                                    	     	   $	  	          
     	   H	  	 	              	   p	  	 <	                   	  
 `	       	      	     	      	     	              	   	                
 	       
      
    ,
                        T
      `
    p
         |
              
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       
                    
        H
  
              
  
           	         P      \    l        x                     (           )      +      	               D              	                (      4   D        P     \     l                            	      	        	          
      
     
      
     
        
 >   
      T  
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                            8            
      
    
                (  " A   !                 X     d     t                !     $    #         '    &                               L             x      P             @                 4        p   ?                d                            B           	                !                           <      H   # X         d                    0                   t                                              (      ,     +         '             H      T     `    p         |                                       <             "                        $                    
         D  	    P    `             t                                       (           "                        P   8              ,              H      T    d         p      |                           $     '    #        *    )                     8  
 <         (  	    4     @    P        \   
 l         x                         !      %     (    $        . :   +                                  (      4   	 D                `      l  :    x  >     A     =          T             	                                                           "    $   '    0   ) 	 @   (     P   &     `   !     p         |   5     2                       !          !       !          !       !#      !'      !,      !. 	    !-     0  !+     @  !&     P  !!      \  !7  l  !6    B |  !    
    !=    !A    !?       !:        !              !             #        #   \  #              $    $  $!    0  $&    <  $( 	 L  $'        $%        $              %      %$      %&     % t             &      '      '     '     '         &                	              *     *          L  +  \  +       h  +   t  + 	   +        +         ,      ,              +	 @             .    .          .    |       .     .    $  .     0  .%  @  .$     P  .     `  .      l  .,  |  .)        .              ./          /       /          /     /      /       /%    /$       /     $  /      0  /)  @  /(    B P  /    
  \  //  h  /3  x  /1       /,        /              ./              0      0               .	              2    2          2   0     (  2   4  2&   D  2&      P  2(    \  2+    h  2.  x  2-        21    20         24      29     2; 	   2:       28       23        2(        2(    2         2C  0  2@      D  2              2F   X     d  3       3 x         3      3&     3&        3(      3+      3.    3-        31    30         34      39     3; 	 $  3:     4  38     D  33      T  3(      `  3(  p  3      |  3@    3?    B   3    
    49    4=    4;       46        3              2F         !     5      5               2	                   ,   $                ;      ?     ?	 t  "         @   $  @          A      A     A         B #     B       B     B      X   B         0   C #   <   C   H   C     C         C $   $      x   D #      D     D         D l   %   %      E'      E&    ?   E         E            E	    &    !  E    '   "  !  F+ %   (!  F,   8!  F+      D!  F0 !   P!  F1   `!  F0      x!  F0 '   !  F   !  F    !    F      $  F
 l!  (   (   !  G  !  G       !  G     G             (    "  H  "  H      "  H     H    "  8"  I    D"  I #  P"  I!   `"  I!      l"  I#    x"  I% #   "  I*    "  I, 	 "  I+     "  I)    (   "  I4   "  I6  "  I5     "  I3      "  I#      #  I#     I        I     ,"         "  <#  L    H#  L    T#  L #   `#  L  p#  L    (   |#  L!   #  L#  #  L"     #  L        #  L& #   #  L+   #  L- 	 #  L,     #  L*    (   #  L0   $  L2  $  L1     $$  L/    	 4$  L%        L     l$  L     0#              M      M `$          H	 !  #  D$       G	 !  !  $   $  A #          $  P "      P     P     $  &       %  ; !   h    $   %  S     ,%  S %  8%  T    D%  T &  P%  U    \%  U  l%  U    '  x%  V    %  V (  %  W    %  W )  %  X *  %  X +  %  Y 
   %  Y    %  R      R
   &  R %  )         [ *   &  [   &  [     [         [
     &             [ *   %  ,&    |&  [
       H&  C   [    ,     \  &  \     &  -     \	     \	    )   &    '  [ `&  &      )   &  ^     ^     $'  ^     &  .     ^  H'  ^    )   '  )      _
 	    _ <'              9                                                                                                                                                                                                              l                 %   V                                                                                                                                                  m                  p         q         r                    s                   r         o      9           The level N must be >= 1.  @ 0 9        4   DirichletCharacter: wrong number of defining powers. Y Y 9        4   DirichletCharacter: wrong number of defining powers.  ̀ 9       9        9                                  T                    9           zeta W W 9        8   COMPLEX: By entering a negative power, you've elected to  x T 9        9   work with modular symbols over the Magma complexes.  This  0a 4a 9        7   is a very bad idea with no practical value.  Good luck. [ 9           Can not create a mod    9            character of degree   |] 9           .  | $ 9       9        9                                  T                    9           a  l  9        %   Invalid character: not enough data at   9           phi :=  T	9           pow at ? :=  i := ",phi;   :  
         zeta is a prim  t ? :  
         th root of 1 f  # :            Invalid character definition at    4 :        (   Invalid character: not enough data at 2.  P D :        !   Invalid character definition at 2   , :        !   Invalid character definition at 2    :  .        $  (  ,  0  4  8  <  @  D  H  L  P  T  X  \  `  d  h  l  p  t  x  |                                      :           N   x :           pows  ; 	:           p  Z Z 
:           r tElt,   :  
         allowcomplex  , :           fac X  :           e de e.    :           m    :           n    :           i   TT :           std v Gcd(r,:           F  ^ ^ :           zeta W W :           C is a very :           i   L :  
         Zr ta := GF(p)!1;  :           s   4 :           ps  d  :           a  l  :           z <a> := GF(:           ZnZ    :           U    :           f    :           Ugens  H :           i  ( H  :           gens enerato!:           ims / DON'T ":           i  X  #:           pn []; i)@@f$:           offset ]];  %:           pr = 0; i][1&:           j    ':           phi P L (:           g if; f; (	):           im en combin*:           j et := 0;  +:           nu    ,:           pnu  @ -:  
         G nu := pn[j]; 2];  .:           h    0 /:           v , h := Uni0:           eps ;   1:           a  8 X 2:                3:              $   f  ::  
           teristic %o    5	5:  
         allowcomplex        4:                                       H    6:           DirichletCharacter 	P~	ʸ7:                                           e    <   |    H   |  X   |         |    l      x   |* 9    |)         |             |         }       }7      }         ~      ~             ,  | 0                                        $   X     h        t                                              L                 @                    t            (      4       @  &    d  6   X         # 7        	     L                  8:                                                f      9:        '   There is no field of characteristic %o. p ;:  
                  <:           N   T =:           degs 
 	 >:  
         characteristic  @ ?:  
         allowcomplex   @:           l acter creaA:           d    B:           pows egs);  C:                D:              $   f  E:             |         $          4      8  H    F:           DirichletCharacter 	    ʸG:  *                                              <       H        l   &   `   6    0   8 7        	     T                   H:  
                 f          I:     (  ,  0  J:           N  h  K:           degs  0 L:  
         allowcomplex   M:                N:              $   f  O:           D  L           H        @  P          H    P:           DirichletCharacter    Q:                                         0       <    7         	     $                   R:     L  S:           N sic; hletCT:                U:           \  p   `     h        X            H    V:           DirichletCharacter 		ʸW:  :                                      0      <                         L                $   X                                 @                                                                                 $          d     p                              P   X              
       (            4    3    ?  *    @<         <  >  <                                   p      |                                                                         d          $     4        @      L  !   h              t        %            '      (     '         '                                                ,    h      R  |  $       X  / |  .     |   <  L                                     
 	                   X:        d                              r                            s      Y:        -   DirichletCharacter: The level N must be >= 1.   Z:     l  p  t  x  |  [:           N     \:           p  l  ]:           d  	 
 ^:           e   < _:           std  div p^V`:                a:             h                               H    b:  
         Evaluate   X c:  $                                       0       <      H     X                	     $               d:             e:           eps ̌ Ќ f:           gamma  4 g:                h:                                         H    i:           Evaluate e(eX!	!	%	ʸj:  D                                       0       <      L   $      d        p   '   X   +    |   *                           -       .      -         -          	     $               k:  
                            l:             m:           eps   n:           n    o:                p:                                         H    q:  
         Evaluate e(e%	H%	r:                                        <   
     H       0       T     d   	      p                                                                   	             $              $       
       	   H       T     <      `     l     x                 	     0                                               !          <          ,  '    8  +  H  *         &              |     d                                                           p             !           ,               
     	                       s:                                      r                             p         m          t:                 u:           eps d  v:           n   | w:  
         v rn (eps`F)!1;   x:           i   p y:                z:                                         H    {:  
         EvaluateAtp "	 "	|:  2                                       0       <       H   &   X   &      d   (    p   )      (         ( D        	     $                   }:                ~:            :           eps D H :           p    :           n   4 :                :                               8          H    :  
         EvaluateAtp (	((	:                                        0   
    <     L   	      X                   	     h         $   t                     
       	       	                                          
   `           8      D    T                        |  
                    
                         #     *                                 p                 ,                ,       D                        E               	     t              :  
      r         q          :  
      $  (  ,  0  4      :           eps  | :           p    :           n   @ :           pn  |  :           i    :  
         X `pn;  ial then  .}:                :           D  \   H     L        @  |          H    :        	   Conductor (e a*	0a*	%	ʸ:  H                                      0                  	     @         $   L                             t                            P          4                    #    "     $      =         H           \          |              
   L   p                                        4             	                                              P     \              x                                                              	 l                                       <     H    X         d                                                                              t               D      (     4     P              `      >p                                    	 0                                             %                        D              (                    p                        d                                               	                                8  "    D  &  `  %       ,      p  !    >                    T                                                                  	     8      D      P     \    l                     	      
             	      
                                               (     4    D      
   P            |                
                `           
   ,                                    
 	                   :  
      s                     :     P  T  X  \  `  d  h  l  p  t  x  :           eps  h :           N rn 1; eps):           std  P :  
         R Eltseq(eps`std);  :           h  ܑ  :           f  @ t :           v     :           fac .	(	:           i   $ :           p  @  :           d  $ ؏ :                :                                         H    :  
         CanReduceModM  x :                                        0   !   <   !  L   !         !    `       l   !  |   !          !! 
    !          !&     !#         !               " 	    "      4  ! $                $     $         % 	    %       $    $         X  '   d  '     '         ( 	    ( t      ' L             +
       +    +    
   +         +"     +     	    +                   :                                     :             :           eps c;  D :           M  \ ( :                :             x          #        P          H    :           AssociatedModMCharacter ʸ  \ :  :                                     0   3     <   3  L   3        3           4 	    4 \       3 $   h              6     6          7         7? <    7>        70    7    7     	    7      h  6              (  :   4  : :    :          ;      ; D             :   P           =       =    =        =         >      >            P  =                B      B ~   B        B         C      C ,             B   8          H$       H(   t  H,      H+    H'         H#                H6     H:      H9      H=    H<         H@     H5      ,  HF     HC        T  H   <  H    `  H    l  H  |  H         H     H         H
   H             H    h         H
           0  H            M     M       M P    M      P  M           N
     N D         |  O
   d  O       O   t  O p          R     R    R        R     R        S 	    S     S        S       S   ,  S  <  S      L  S         S     S       &          R   X           U     U    U        U     U        V      V     V               8  U            (  Y     Y        Y        X  Y8    d  Y<  t  Y;         Y7               Y%      Y*     Y-     Y)         Y$                  Y2    L         Y$           D  Y!   	      4  Z     Z         Z (  
     d  Z8 
   p  Z<    Z;         Z7          
     Z%      Z*     Z-     Z)         Z$                  Z2    X         Z$           D	  Z!        @  [    L  [  \  [         [              \ 
    \     \        \      \ 	     \$      \'      \*    \)       \#     	  \      	  \         \     \     x  &       
  [    4  (	     h	  _   t	  _  	  _      	  _     _       	  `   	  `     `      
  ` 	        	  `   	  `     `     $
  `     	       `  H
  `       
        `#  h
  `!     <
       `     `       \
    
  _ \	  	         
  d     d
      @  d 
        
  e   
  e  
  e      
  e     e        f      f     f                 e 
  $         d  h
   p  h    h         h4    h3    ?  h*    @  h         h>    h          h           0  h X           i' <    i&        i        i         P  j    \  j     j       x  k      k      k      k    k       k        k         k l         j D            m     m         m    ,  m!   H  m            T  m    `  m%  p  m      |  m'      m(     m'         m'     m            q     q       q     q           r F   r        r         ,  s# B   s"       H  s    T  s    s         s     <             s       d       s             s           t      t        t            u     u      u   (  u    4  u   D  u         u      u                  u      P       u       l      u           w ?   w        w          w          w             x    0  x      x      x         x     $             x      @       x       \      x t         y      y B  y       y         y               z      z      z # ,  z     <  z       H  z     z         {      {	 X              z   d         y      |      4      C B  B       7         3                          $       0  $    <  ' # L  &     \       l                   
                   .      |       
                                                    (   < 8        D      P     \      h     t                                      !           "                        
                   "         H  
         C                     X       
     
    !   x       ,  d      !      
 	                   :  N                                 q         q         q         s         l                                                    p                                       m                  p         q         s         r                              r      :           AssociatedModMCharacter: M < 1.  :        K   AssociatedModMCharacter: Invalid M; character extension not yet programmed. x ( :        @   AssociatedModMCharacter: there is no associated mod M character.  ԙ  :        ;   Magma's unit group function is not as canonical as I hoped. 0 8 :  &                                                     $  (  ,  0  4  8  <  @  D  H  L  :           eps   :           M  Ч ܧ :           i  $ , :           pn    :           es oving fac:           s   d :           N  H T :           facN   D :           i   , :           pN   P :           facM   :           i     :           pM   , :  
         i i in [1..#facM]]; :           t     :           d ce the mod:           e = 1; (M,2):           p   H :           std  div p^V:           f //////////:           U   x :           u  l t :           a  ` l :           ZMZ   :           ai    , :           abar   :           UM    :           h  d l :           x  ԭ ح :           red   :           i  [h(x) : x:           i  @ H :           ims ;  "Magm:  
         epsM ators(UM)]];  :           a    :                :           \  `   `     d        X            H    :           AllStandardCharacters  < :  >                                      0   &  @   %    ?P       @             $                        ,   t           5       9     8         4                                       (      4     @    P        \    l       |                  "     %    !        *    (                 
                   /              
           \           L       
         @         |  
      
                                	            '                            p       4        @      L  !   h              t        $           t   $                                                                         
                        $       
       @    8   X  	               
                                                                      	       T               \     h   
 x                                     %     '    $        *    )                     <           0                 	   $    l   P            x        
                           	      
                                   
                 
                             L  
     ,	   l  4  X                                                         X  
           	       ,        8               	           H         |                                      p  
      
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  	                           	                             l	  	   x	     D	     	   `	       	  
    	  
   	      	     	                 	          	   
           l
       
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            
  
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  
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    
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  X  	               L            	 	      
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                    (             <  t  
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 	                   :           :           N on; ;  :           std x(  :           i   8 < :                :                          	                  H    :           AllDirichletCharacterClasses  h :  d                                      0      <              X   ! 7 h                        	     L         $                         
            `                                     '  ,  &    ?<      @         l                L   `                        :                                                        "  (  !                      P  +    \  -  l  *      x  3     0                 D                                                                                   H      T    d             x               #                                                          <         0        (    $  	                                    h      L          2      6    5         1                             $    #         ' 7             
                  ,    x      \  
       (        
 	     @              :                       :           N sic; chlet:           std ' |; :           n  x  :           i );   x- :           v  ,< 4< :           m  d( " :           a  8" @" :           ind  < :           i  (  :                 ;              T                     $      H    ;           Print  chlet;  D                                      <   
     H   *   0   .       -       $       p                                                                             d                     ;                                    s          ;           Mod %o Dirichlet character:  2 2 ;  
         trivial.       ;       ;           eps 0& 8& ;                	;         
;           0  ,  4     8        ,  T          H    ;  
         LinearRelations     ;                                            5    <   #    H   &      "             p       |                 	     d                  0           	                                  0    $                                  L     \         h  !  x            %     '    &       $    /           *      2 6   -        *         *   4   @        $   c         	                       ;                ;  
   <  @  D  H  L  P      ;           P     ;           prec   ;           f  , % ;           i )	.	dC!	;           X  ! ! ;           M  " " ;                ;           `     d     h        \            H    ;           MonomialsOfDegreeD_recurse  87 D7 ;  R                                      0     @          L        	        h       t                   	     \        $                                                  !                           <      H   #                  0                    X             t                 	                                                            <  	    H       
              0                   X              t    p            M      P      L               %      '      -     ,   ,  ;     8  ?  H  >         :             p  0    |  2 #    1         /     d             5             /             ,              ,     
      $         	                  G              	       <       T                                       h                  G      J     L    K         F             @  3    L  6 	   X  8  h  7      t  ;     5          #     %    $    	     (    '    
     *     )         "                  . 
   4         "                                  A 	     4              P  6       5                               #                                          $   G    0   J   <   L  L   K          F             t   3       6       8     7         ;      5          #      % #    $          '     &          )      (          "                   .    h          "       4              L              A      h                 6        5            	              !    	  !      !
          	    !               ;        l      ;     l  p  t  x  |                      ;  
         P sic; l(M); Integer;           D  h1 d1 ;           R      ;           i  T \ ;           i  " "  ;           Q   8 < !;           d  3  ";           i  7 7 #;           QQ i] : i in$;           d  P& T %;           f  (<  &;           serpart ( ';           d  $$ 0$ (;           m  x(  );           polpart t *;                +;                                            H    ,;           MonomialsOfDegreeD 	O$	ʸ-;  0                                       0   %%    <   %' R  L   %A        X   %E  h   %D        %7       $   %
      %$     	    % x                   .;             /;  
         P eturn rn  $ $ 0;           D  % % 1;                2;             L                               H    3;           RelationsOfDegreeD  A A 4;  >                                       0   *    <   * G   *         * $         l   +   x   +     +          + H   +          +&      +(     +'    	    + `                   5;                 6;           P sic; ialsO7;           D  ' ' 8;           prec ( \! 9;           m  ' ! :;                ;;                       	        $          H    <;           RelationsOfDegreeD 	Xm'	ʸ, m[2]; =;                                            0!    <   0 y    0         0     0              0    $   L        0       h       0         0              1       1 G   1      P  1            2     2   $  2       0  2# H@  2    2    2        2         t  3          3#    3"        3      |  3 d           49      4      4     4     4'      4+     4-    4,     (  4*         4&             P  4   \  4    h  4  x  4         4      4    4        4         4     D             4!             4         )   4         4         4      4
                  44      ,       4
       H  	    4 `                  >;                ?;                         @;           P    A;           D   - B;           f  # # C;           prec  $ D;           m    E;           r  h, D F;           R    G;           b  ( P H;           i    I;                J;           0  @   4     X        ,            H    K;  
         CohenOesterle +	4-	L;  *                                      0   >     >      p   > $         `   >.     >-         > T             ?     ?        ?             @3       @'      @)     @(         @&                   @.               @&            D  @    P  @    \  @  l  @         @               @     8             @!             @             @            B     B           C   $  C 
 4  C      @  C     C          D      D P        |  E     E 
   E
         E     E         F      F           E p            C   \          H     H   	      0  I   <  I 
 L  I      X  I     I         J      J h  	        K     K 
   K
         K     K         L      L   	        K           0  I $  t          O          `  O   
       P  [ <    [        [ D         ^     _      _    _         _               ^      ^     ^"    ^         ^%      ^*     ^-  ,  ^)       8  ^0    D  ^5   P  ^8  l  ^4    
     ^      ^         ^     `             _      |      ^            ^       ^         `      `5     `4          `:   ,  `<  <  `;      H  `> 	 X  `=       d  `C     `@          `      `"     `         `   t             `'            `             ` )   `       `    	 (  `    	   D  a    @  a5     a4       \  a:   h  a<  x  a;         a> 	   a=        a@ 	   a?         aE     aB          a      a"     a         a P               a'    4      P  a           (  a ) `  a     p  a    	    a     	    ] t              M;         @                @            	   8          @        N;           @  \          D        <  T          H    O;           lambda /3;  P;                                       0   P    <   P
  L   P	        X   P :    P        t   Q     Q          R        R      R     R        R          R!        R%      R+     R'        R.    R-     (  R"    	    R     	    R      T  T    `  T     l  T   x  T    T        T"    T       T        T     	    T H       Q	 h   8        W      W       W      W  ,  W     <  W        W     	    W	        P $     L                  Q;     H  L  P  R;           r f = 0; luaS;           s    T;           p    U;                V;     \  `  d  h  l  p  t  x  |              W;           eps c; [m[2]X;           k  t  Y;           N ohenOesterZ;           facN y y [;           f    \;           p    ];           q  L D ^;           facf ctor(ep_;  
         gamma_k in facN]];  `;           mu_k |  a;           lambda /3;  b;           K     c;           i  *	+	d;           x  Y Y e;           x  @ @ f;                g;                                         H    h;           DimensionSk  return rn  D  i;                                         0   h# < @   h"     P   h       \   h,     h)          i      i l               h $   x              k ;    k         k             l
      l     l      p  l          m     m       8  n    P  n    ,  n      n     	    n D       m   `            p      p     p    p       p       p      p!    p         p          q 	    q     <  p           D  s   T  s      l  s    x  s   `  s     s         s"     s$    s#       s        s'    s&          s:       s>     s,     s9    	    s*      0  s         s 	    s 8                  j;  
                           k;        R   DimensionCuspforms:  Character must take values in a field of characteristic zero.  Ⱥ  l;           m;           eps 
 
 n;           k  7 7 o;           N   Ĺ p;                q;             \                               H    r;  
         DimensionSk \ 07 s;  "                                       0   z) 7 @   z(       L   z- I   z     	    z $                   t;             u;           N sic; ers()v;           k   ; : w;                x;             X                               H    y;  
         DimensionSkG1 +	+	z;                                          0       H       $   
           	     <               {;             |;           N  D H };           k  S S ~;                ;             L                                H    ;           DimensionS2 8+	h+	+	ʸ;                                         0      <    I        	     $                   ;       ;           N  ] ] ;                ;                      (          <          H    ;           mumu   ;                                         0    ( @   
       L     \                p       |         #                                                    $                  $                          h            D              `  	   l    |  
                                                                                                       $            T    8         8  P        
 	                       ;  
   %             $          ;        &   mumu(N): N must be a positive integer.  H ;     ,  0  4  8      ;           N  h  ;           p   ( ;           m    ;  
         m ctorization(N);  ;                ;           H  `  L     P        D  `          H    ;  
         DimensionSknew ,2); ;  b                                       0   E     D       L       X    I          t   +      +         -        /       1     0         -         -    h         "                      @              7    $        P           )    
     	     4              ;                ;     T  X  \  ;           N on; -2*p; ;           k   ( ;           M  l t ;                ;           l  `  p     t        h            H    ;           DimensionSkG1new    ;  b                                       0   G     F       L       X    J          t   -      -         /        1       3     2         /         /    h          $                      @              9    $        P           )    
     	     4              ;                ;     x  |    ;           N sic; mensi;           k  @ t ;           M    h ;                ;             @                            H    ;  
         DimensionAll   ;                                         0   ' K   &      t    $        d   #                    T                                     (                                             
             D          H      T    d                               !      %    $    <                  "    !    L          7      :      6             <  !    H  %  X  $       d  ( It            +      -    ,        *              0             1                     )                                 &       h      <  (        
 	     \              ;              ;       ;        ;                                  T                    ;           t  p t ;                         ;           N sic; mensi;           kmax  , ;           eps 4 < ;           R    ;           t  p t ;           d = &+[Dimen;           i  `  ;           k     ;                B        B                 %                    ;          ;        ;                                  <                    ;       D    ;        ;                                  <                    B        M                            $                            B           : ;     ] @    ;        ;                                  <                    ;          b  ;     :        ;        ;                                  <                     ;     G  )      ;        ;                                  <        (  ,          ;       @      ;        ;                                  <        4  8          ;            ;        ;                                  <        @  D          ;      _      ;        ;                                  <        L  P          ;      jW     ;        ;                                  <        X  \          ;      F      ;        ;                                  <        d  h          ;     
 b8     ;        ;                                  <        p  t          ;     9
 1     ;        ;                                  <        |            ;     qv h     ;        ;                                  <                    ;     	 I>     ;        ;                                  <                    B                                                                   B              @  ;           ;        ;                                  <                    ;     @      ;        ;                                  <                    ;             ;        ;                                  <                    ;             <                            H    ;           FindSupersingularJ   + (+ ;                                       0             T          $             l   
   x                                             (      *     )           - 7   '       3    0      ,                   @     L     X    h          t                                                                                             	    	         `   ,              T   <                  ;  
      @B                    ;             ;           p    ;           s inElt l ;                B     ,             cke.m       B                 B                    ;           x  B B  <           j  T P <            k	    B                  <            <xB             $      <               $ <           L  < <           <IPCP <  
         hHnaZ   j$	T%		<  
           :FC8  ~'	 h(	
<  
            @i΅ (%	X&	<           <IPC B  
             @  (^!	pF"	<  
           gxגVl$	T%	B  
           @    }	  pF"	<  
               =ob"5 )	<            <x<  
         hHnaZ   0'	 h(	<  
           gxגV*	+	<  
            @ħVG'  4-	<  
              Sw/)	<                  0r^   `!	pF"	<        "zo9    <  
           :FC8  0*	+	B  
             @? )}	  X 	<  
              Sw/T%	<                    `h&/c  %	X&	<                <  
            @i΅ u$	T%	<  
               =ob"5 T%	<                  0r^   z$	T%	 <                    `h&/c }$	T%	!<                      ܲCHH$	T%	"<           {2   D C        Y        $ $<           PF  C                   &<             Mks< '<           9CN $ (<  
         `	   ؞$	T%	)<  
         ՗f, X$	T%	*<  
         0G\Z*ɰ4أ$	T%	+<  
         *յ2?݆   T%	,<  
           :ԙ"u54.3  T%	-<  
            \:#YW  T%	.<  
         `	   $	T%	B  
         x               0<  
         )',e T%	B                   F        2<             X%?^  $	T%	B                                T%	4<                W07   T%	5<           {2    6<  
         ՗f, $	T%	7<  
         )',e X&	8<           F{W*&޷  %	X&	9<             =:gξ`u-)y%%	X&	:<              {YWB;   X&	;<                Xj X&	<<                  p1duX&	=<        "  ( ><  
         0G\Z*ɰ4P
&	X&	B                    B        @<             =:gξ`u-)y%X&	X&	B              B              B<                hZ^Li҇X&	B        EF        5      B        D<                    PyTd  &	X&	E<           PF  F<  
         *յ2?݆   X&	G<             X%?^  H &	X&	H<              {YWB;   X&	I<                hZ^Li҇X&	B               B        F        A          ʸ C                   L<                      TNk7%*8,&	X&	M<        7R|  N<  
           :ԙ"u54.3  X&	B                                  P<                Xj X&	H        H        %      H     %         (ʸB        S<                      s7' ]=&	X&	T<             Mks U<  
            \:#YW  X&	V<                W07   X&	W<                  p1duX&	X<                    PyTd  @L&	X&	Y<                      TNk7%*$	T%	B  
      ,               B        H        B                ]<           |  @                x            H    ^<           TpSS 8*j^7 +_<                                       0              |    $         `      l                  T                       8                       "                     #                    0                    X      d     p      |                                 L  
                                                       ,     8    H      y             
                         X      
       t  m   	        (     %              %     $      ,                            \              P               D                           t           |                 # 	                  y                                	          P           m `        l  ,     )         4        ;     * 
     -     /    .         )          
                          ,                                     $      <              X            p             6 
                    6    
     	                       `<                                                    a<           Char =  @ b<           p =  
 
 c<           j =  	 	 d<           fac =    e<                                 f<           p 8106918258g<           j 5840000000h<           F 5721163681i<  
         R Parent(j); 4137572j<           S 0000000000k<           h 1032241603l<           phi z z m<           fac x x n<           a  | t o<           a  | x p<           a  4 ( q<           i    r<                s<             L                               H    t<           Mestre   u<                                         0      <            	     $                   v<       w<           p    x<                y<             h                            H    z<  
         Mestre e(p,1);  \ {<  "                                      0       <     L         X                  $           9              x                                                 l                         $  &   0  ( I@  %      L  + 	 \  *                            2                                 $      (    '        *    )         #             4      @    P         \      h    x                               (                                                        0               
  P       $         t         D        
         h                                                                    
           <                `         0        
 	     T              |<                 2          5         _          }<           Not programmed for M ne 1.    ~<  
                    <           p  4 ( <           M    <           D r "Not pro<           B +1);   <           i  P H <           X sis(D); eg<                <              <   $     (  
        T          H    <           TpD c; 0,0,0<                                      0   %      %      %       $      `   &
   l   &   x   &      &      &      &               &        & T          '       '       '       '    '    (   '
      (  '     '        P  (   8  (    \  (     (	        x  ) y    )        ) l           *,     *.      *- M  *+         * 0             *            *
     *
               <  ,   $  ,    H  ,     ,         , 0         ( D    X      ."         .%     .      0  .          /      /)         /, L   /         /.      //   $  /.         /.   h  /        P  0    \  0      0               1       1     1      1      1     1    N   1      P  1 x           2       3     3       3  ,  3           3             3  l  3     @  	     3    3        `       3 
     3  H  3       3       3   L  3       -          4      4       4     4      4    (  4   8  4        4     \  4        4  4    	   	      4    4     p       4       4     4      4      4      4       4               4      4     4   	  (  4      4(  |  4$                 2           0
    D          7    7           7	       7
     7	            (  '    l             9
     9      9      9     9    	    9               <  4      _      %             ]         2          ]         ]                    ]         ]         ]      c             ]         ]      c   	          _         _          <     ,  0  4  8  <  @  D  H  L  P      <           X    <           p    <           d    <           V  @ < <           T    <           i !	!	ʸ<  
         S i in [1..d] do Alg<           j    <  
         --temp--    U L <  
         --temp--    U L <                <           `  h           d        \  p          H    <           TpX c; ];  <  $                                       0   ?    <   ? L   ?        X   ? \    ?     	    ? $               <     h  l      <           X  ,| (| <           p  pr dr <                <           |  `               x            H    <           MestreEisensteinFactor 	ʸ<                                         <   D    $   D    H   D     D         E      E X             F       F    F          F      F 	    F        F        F x            G c    G        G          (  H 1 8  H      D  H  T  H          H h       t  H"     H'    H$         H              I     I      4  I            J      J   J         J     J 	 $  J        J        J         T  K    `  K c p  K        K         K H         H          M 1   M        M     M         N      N	            (  M               P  H  P            P     P        <      D 0   d             R
   x  R       R 	    R                   <        `                  `         `          <        5   Not enough Hecke operators to find Eisenstein series.   <                 <           X  q q <           p  m m <           T  2;  4v <           V  Tk Dk <                <             L                           H    <           MonodromyWeights  d \ <                                         <   W    $   W    H   W     W        d   X7 Ot   X6    2    X         X;     X:    P    X      L  X X            Y,       Y#      Y                   Y'            <  Y             Y         Y        Y ,           Z:    x  Z-      Z/    Z.       Z,    B    Z"         Z     l             Z5    `         Z            Z     4  Z            Z     Z        (      W 0              |  \
   d  \       \ 	    \ p              <        ^         ^         ^      <               <           X sic; en;  <           eis l d <           e    <           n    <           e  h d <                <                                         H    <           SupersingularBasis     <  >                                       <   a    $   a    H   a     a        d   b   p   b    b         b X           a 0                 d
      d       d 	    d                <  
      ]         ]          <             <  
         X sic; ghts;  ( <           dummy  ` <                <                      	        0          H    <  
         Decomposition       <                                        <   j    $   j    H   j     j         k      k X           l!           l+ y    l*        l         l                l x           m   8  m            n     n : ,  n          n @  l     L  n  C\  n     l  n         n               o      o    o        o            p      p*      p6      p=    p5       p/        p&          p      p                p      (       p       D       q;      q= \   q:    ^   q1        q!        q x          r    r        r     r        s    $  s#    0  s*     s"     t  s               h  t       t    t     \  P           u     v      v!      v8     v:    v9         v=    v7    c   v.        v#       v       &         @  w   L  w  \  w      h  w     w        x      x#     x     x  &          z      z#     z       &           w 4          u             }   (  }   4  }  D  }      P  }     }         ~)    ~&     `       ~      ~"     ~        ~              }   l           r   @     $  p    \                               X  n             x       L                    l      j 0   d             
             	                       <                                                                        <         <        <                                  P                     <                  $  (  ,  <           X  t l <           p    <           Decomp  , <           Irred   <           T  ̩ ȩ <           V   t <           V  \ X <  
         fact V)] ] do   <           f  t p <                <           <  @   @     P        8  d          H    <  
         TestDisc p; if   <                                         0    9          l    $       \                P                                        & y    %    L             )       .      0   -      $  )         )               P  /  `  .    
p         |  6     3          	    	         D                  0       
 	                       <        L                                          <                     <        <                                  <        D  H          <     T  X  \  `      <           p  c xc <           X  t^ p^ <           q  8\ 4\ <  
         T n [2,3,5,7] do ate<                <           p  h   t             l            H    <  
         AtkinPolynomial I <                                       0   
   <        H     X                     $             
          x      R     #                         D                               |           8                  ,           l                   `                                 0                                                   D                      d     p                X                                     +       .      *              	      	      
    ,   	   8    QH        X  
         
                        % 	     d                  
     
                                                 0        	  	       L      X                                   
                              	                                !  ,  "   <  !      H  !   T  %  d  $     t             
                              	                               !    "   $  !      0  !   <  %  L  $     \       l      
   x              	                                    !     $ 	   "                  (       8      
   D      P     \   	 l       |                            ! 	    $    "                               
              (   	 8       H      
  T      `     l     x  !       #    "        %    $                                     
     t                 @      <	  
       	  ) L	       \	         h	  
     t	      	    	       	          	                                 	     
         	  )         	     	              <  $                                                                                                                  <       <        <                                  T        x  |          <           a  > > <       <        <                                  T                    <           x  : : <       <        <                                  T                    <           j  7 7 <                               <           n sic;   N <           p  G G <           K  A A <  
         P (p); 2*n; UPolElt <           a  > > <           R  h; `; <           x  : : <           Q   8 8 <           j  7 7 <           i  X1 T1 <           B oose i <--<           i   d  h  <           m    <                <                                            H    <           SupersingularPolynomial   <  ,                                       <       $      L         X     	 h           t   " R        	     0                   <       <           p sic;    <                <             l                             H     =           SupersingularBasis  `  T  =  n                                       0      <     L       \                    $                                 5 S   4                                                      0                   
                          @       
       \  	     t              =                =           =           p sic; Polyn=  
         Fx -> SeqEnum     =           a       =                =           (  h           ,        $  @          H    	=  
      
   RibetRaise  P  L  
=  b                                       0       <      H    	 X                     $                              `   |                   	                                  	 $         0    	 @       P               	                    =     0  4  8  <      =           A sic; toriz=           ell     =  
         f ) -> RngIntElt **/=           a       =                =           L  @   P     l        H            H    =           SerreModPQHelper &	x~&	ʸ   P  =                                        0    x          p   	 $         `    x             	 T            #       %      ' 	    &        "          *           X  	            #      %     ' 	 ,  &     <  "       H  *           $  	         x         " 	   !         $    #        )      + 	   *         - 	   ,       '                     d  	 l  	   	          P  ,   \  .  l  -      x  1    0       *    
     9     ;    :    
   5         A     >    
                         D                
   8                0    0  	 H  	              " 	   !         $    #        )      + 	   *         - 	    ,       '                      p  	 x               \  ,   h  .  x  -        1    0       *         9     ;    :    
   5         A     >                             P                   D                 <      	 T                     
  	                                               	           (  p     4  )    @  +  P  *     `  (     p                         /                               x            &    #        /                $       0  '    <  )  L  (     \  &     l         x  >    =       .                                                   	                   	           0  x     <  )    H  +  X  *     h  (     x                         /   	                            x            &  	  #      	  /                ,	  	     8	  '    D	  )  T	  (     d	  &     t	         	  >  	  =     	  .                     	      	                 	              	       <
             ,
   T         T    
       \
      h
                     
      
  5    
  A    
  C  
  @    U
  4    5 
       
                        
                 P
                     l   8       t                                  5      A      C    @    U  4    5                                                 h                8       P                                                                         
             h        	             	      
     

 H       t                                                 
                           "   p       &    (  +  8  *       D  2 
 T  .       `  7  p  4         "                                &                     4      h                                                      &          	
    <  T         0  P        
 	                       =        \         h         l      =        =        =                                  <        T  X          =        =        =                                  <        `  d          =     p  t  x  |                                                =           HN  d  \  =           f     ܻ  =           HM  P  H  =           g   к  Ⱥ   =           HNM      !=           N   |  t  "=           M   @  <  #=           aM  ̴  ȴ  $=           bN  h  `  %=           plist     &=           p   |  t  '=           qlist     (=           q  l l )=  
         D [1] ne 0];     *=           i  a a +=           fnew ] ] ,=  
         gnew  := D[i];  N -=  
         n if; := D[i];  x: .=  
         i Factor(D,i))))   /=           fcon mNewFac0=  
         i Factor(D,i))))   1=           gcon     : i2=           ans   3=           p    4=           q    5=           l  , ( 6=           i or|for a 7=                8=             X    	             L          H    9=        
   SerreModPQ  !	!	h!	ʸ:=                                        0      <     L   	             `       l      x                                (                 $     !         '            *     /    ,      (  '                              	     <    |   $   H                 p         =                           #     #      # 8    #        #	           $     $        $	          <  % VL  %       X  %     %         & 	    & h      % 0  t           (     (      ( 8    (         (	           )     )      h  )	            * V0  *       <  *     *         + 	    + L      *   X            .      .    .        .      .! 8    .         .	           /     /      <  /	           1    ,  1 =    1      `  1               4   $  4 T               6      6      6      6     6     6              6               6               6
               6 x  	     D  7    P  7" V`  7!         7              8      8% V  8$         8               9 
     9     9      $  9           :      :     :      l  :        D  <    P  <   \  <!     <        < 8             =      =     =!     =      h  =          	    ? 
     ?    0  ?       ?+      ?.      ?0    $  ?3    <  ?5      ?   L  ?*         ?              ?       &          8
    |       7 
   8    	      B
 	    B               ;=        l                  l         l                                                   <=        <   SerreModPQ: Creating and decomposing modular symbols spaces.     ==           Time:   p  >=        $   SerreModPQ: Considering pairs (f,g):   L  ?=         @=        A=                                  <                     B=           f =      C=           g =      D=              $  (  ,  0  4  8  <  @  D  H      E=  
         N eturn  for if  F=           M      G=           s rn [];   H=  
         HN ; utime(); ating I=           DN  |  x  J=           HM  `  T  K=           DM  \  X  L=           HNM  [];   M=           DNM     N=           ans $    O=           i [<N,M,[<0,P=           j       Q=           f       R=           g       S=                T=            X  L   \       
      T          H    U=  
         SerreModPQTable L  V=                                        0   H    <   H W   H      x   H $         l   I      I      I `         J      J       J)       J2      J          K      K     K          L
      L
    L      $  M    0  M      M             X  M) 9    M(          M	      M L  h             M      t       M             M          N      N     N         N             (  O   4  O 	 D  O       P  O  `  O         O               P      P    P         P      P    P       P         P    P          P!          P%    $  P'  4  P&       @  P*    L  P,  \  P+     l  P)       x  P2 :   P/         P!             Q       Q. 5   Q*        Q7 5   Q3         R       R"    R!    X  R    5 (  Q=      4  R* 5 D  R&       P  S     \  S"  l  S!    X|  S    5   R.        S* 5    S&         Q      	    T      T  5   T    
    T( 5    T$      8  T   	        U 	   ,  U      U   \  U          	      V     V     P  Y          P	 |            O
      x     N              Z     Z W   Z        Z           [      [   <  [      0  \
      \
     \ $                  W=  4      `         d         h         l      c             p         t         x         |                                                            c              X=           w   Ī    Y=        !   // Serre's conjecture modulo pq.
   d  `  Z=           // %o <= NM <= %o

     [=  
         SERRE := [*
     \=           SerreModPQTableNM(" l_ h_ ]=           ",  ] ] ^=           ,  X X _=  
         ); quit; quit;  @T `=           echo '  Q a=  
      	   ' | magma  O O b=           System( i+1.c=           )  L L d=           a  XG TG e=           []
*];
 hE f=                             g=           name ;  X  h=           NMstart odPQi=           NMstop    j=           out P  L  k=           p   (  $  l=           s out;  "SERm=           i     |  n=           j   l  `  o=           cmd  ` ` p=           go  pR `R q=                r=         s=              L                          H    t=           SerreModPQTableNM $	X/"	ʸu=  <                                       0   b    <   b W   b         b $         l   c   x   c       c$       c& Z   c#         c `         d
      d
     d                v=                       c          w=           a  ,: : x=           %o,
 8 8 y=                 z=           name @ `@ {=           N SerreModPQ|=           M t, @ @ }=           out ; ; ~=                =         =             `        4          d          H    =           IsIntersectionGraphConnected e );  =                                       0   u     <   u   H   u    T   u      u      u $                 w       w 8    w         w x            y     y         y             z	  `  z                    [(         4  $     !          	     D         P           	              x                                         4            	                        T                 $   H          	                               t                                                                         D   
   P    `       p                       9 	     ;    :         > 
     @    ?    U  8       $          G    D                   	   0     <   
   H     T      `  4 	   l  6  |  5         9 
     ;    :    U   3         $              
        4         &                " 
   $  $ \   !                            8             
   ,  P     
 	      h              5                                                                    h       D    T  
       `  ( [p  '             	     8              =                                             $         (         ,         0          =  
         Analyzing ( ted.} **=           ,  + + =           ):  * * =        =        =                                  <                     =           <-->   =           :     =           V =      =     8  <  @  D  H  L  P  T  X  \  `  =           N  01 (1 =           k  / / =           M onstruct m=           D  & & =           n rn true;  =           V  ;  // num=           W  connected=           A ..n];  ()|=           B  T H =           i    =           j  ` X =                =           p  0   t             l            H    =           Artin ******=                                              T    $                      H              x                 ) 7              l                                              	       8          X           <      H   1          |   0                    p                                       <                                         0                 $                    (    |                                  p             #    d                             6 	     X              =        x         |                                              =           Artin in weight 5 ing FastTp.} dual =           * Creating Dirichlet Character    =        '   * Creating the space of modular symbols   =  
         Dimension =      =           * Computing kernels P  L  =       =        =                                  T                    =           x   8  4  =                         =           N H  @  =           degrees   =  
      
   zeroprimes rees::Seq=  
         eps  weight 5"; L  =           M   H  D  =           R       =           x   8  4  =           p       =                =             @                            H    =           ToLatex @  =                                         0    (         T        $                 t                                                                     	          0  	                            D            
          d     p                X         
      
    
                          ]                          ^                     H      T  $    `  +     l  - 5|  *    ^             <         	   (           	    	                                	            8   h                          =     %   r       c                                              c                       =           0 f|(x): x) =       =        =                                  T                    =           a       =           %o    ܹ  =           %o^{%o} Զ  =           Type not programmed.     =                =           x       =  
         --temp--            =           F       =           a       =           s   4  ,  =                =              L        4          P  T      H    =           TableEigenvalueList     =                                         0       <    W         x    $         l                `        
                                                               8  &      1    (  4  D  3         )      0               p  	    |   
                                   "      (    '       $                                  	      <      H    X                 t               h       	 0             d                                             T       
      
                    =                  $         (         ,         0      c              =           w   4  (  =           \\begin{array}{|rl|}\\hline
     =  
      
   %o&%o\\\\
      =           \\hline\\end{array}
     =           \\begin{array}{|rl|}\\hline
 v u =  
   8  <  @  D  H  L      =  
         filename n      =           ap n; n s; r=  
      	   colheight   Ԫ  ̪  =           out IntElt) =  
         p \hline\n";     =           i 2; t, "\\\=                =         =           `     d     h        \            H    =  
         ArtinOrderTwo ); t =                                       0       <                      d   ) 9    (       h         +       8      7        +         ;        <      ;         ;                     $      y                                       4             P                              X   t                  $                                       ,     8     H        T  &     #       p     |                
    d                          
         	                       =                =  
   l  p  t  x  |        =           h  m m =           pstop  l =           p  H` 8` =           f  f f =           degs j Xj =           a  Z Z =                =             0                            H    =           Artin2  : a =                                             T    $                  x    H                      l                      
                                                                            (     4   
 D         P             l                  `          $     x                  
                                                                H  	"    T  	%      	!             |  	      	     	         	     p             	    <        	             	- 5   	)         
"     
$ 	 ,  
#       8  
(  H  
'         
!             p  
    |  
     
         
     d             
            
         5    	1        	                                   <       H    X         d  "   p  + 7             0                                         	       8          8                (   1          \                       P                                    t                                      	                                          ( 
   \   	   h                            P             # 
   D                             6 	     8              =                                                                                 =           Artin in weight 2 ing FastTp.} dual =           * Creating Dirichlet Character  G =        =        =                                  <                    =  
      
   degrees =    ( ' =        0   * Creating the space of weight 2 modular symbols ! ! ! =  
         Dimension =    =           * Computing kernels L H =       =        =                                  T                    =           x  8 ( =                           =           N  S S =           degrees Q =        
   zeroprimes grees::SeqEnum,  =  
         i in weight 2"; P =           j  3 3 =           j  . . =  
         eps = ",degrees;  : =           M      =           R    =           x  8 ( =           p  \ X =                 >           23 ic; ubspa>  
         23A VES := [ *******>           29  | t >           29A   
 >           31  
  
 >           31A t	 l	 >           35   | >           35B   >           39    	>           39B ` X 
>           63  d ` >           63B   >           65,A   >           65C D @ >           65,B  @ >           65B   >           67      >           67B     >           73      >           73B p  t  >           85    |  >           85B      >           87      >           87A     >           93      >           93A     >           103     >           103A   |  >           107     >           107A      >           115     >           115B      >           117,A >,    !>           117B     ">           117,B     #>           117C   L  $>           125,A   `  %>           125A     &>           125,B     '>           125B   H  (>           133,A   l  )>           133B     *>           133,B     +>           133A     ,>           135 \  P  ->           135D     .>           147     />           147D   T  0>           161 d  `  1>           161B     2>           165     3>           165A   X  4>           167 h  d  5>           167A     6>           175     7>           175E   4  8>           177 ,     9>           177A   h  :>           188 x  t  ;>           188B     <>           189     =>           189E   `  >>           191 `  X  ?>           191A     @>             0                               H    A>  
         EvidenceCurve     B>  @                                        -      -        $       T   .
    `   .  p   .    :    .         . H         /        /(      /+     /'        /     	    /                    C>       D>           n ;     0  E>                F>                 $     ,          8          H    G>  
         EvidenceCurve   D  H>  J                                         6    <   7	   H   7  X   7
        d   7     7          8      8      8        8     	    8	 t        7 0              6    $            ;	      ;                       I>        (      J>           Curve not found.       K>     0  4      L>           s       M>  
         C ", or "65,A".} ˸N>                O>           D  X           H        @  P          H    P>           EvidenceLabel )	)	:%	ʸQ>                                         0   @
     <   @   H   @     @    	    @ $               R>     L  S>           n   Ȼ    T>                U>            \  L   `       	      X          H    V>           TableEigenforms 0)	:%	ʸW>                                         0   U    <   U W   U         U $         l   V   x   W       X       X       X      V `         Y      Z       ZJ      Y          [      \      [         ]      ]   T  ]      <  ^   H  ^       ^"     ^ 0     p  _   |  _       _"     _ d       `     `       `K     `        a
      a
  P  a         c      c      c          	  4  k    @  k 
     k     k (           p  l     |  m 5   l"        n 5   m         o X  o    5   n        p 5   o!         q X  q    5   p      (  r 5 8  q!       D  s XT  s    5 d  r      p  t 5    s$        l
 d         u      u 5   u        u" 5    u        u
          w      w      w   4  w                x     x     (  Y         c      L              X>  @      d         h         l         p         t         x         |               c                                                                                                                 Y>           w        Z>        >   // Table of weight %o eigenforms on Gamma_0(N) for %o<=N<=%o.
    [>        C   // <Isogeny class, Wq's, h(x), [a2(x), a3(x), a5(x), ..., a%o(x)]>
 t  x  \>        /   // Each ap(x) is in terms of a root of h(x).


 0  ]>        '   R<x>   := PolynomialRing(Rationals());
   ^>  
         Nstart := %o;
  (  _>  
         Nstop  := %o;
    `>        7   f      := [Parent([<1,x,[1],[x]>])|[] : i in [1..%o]];
 H  a>           
Spawning level      ؔ  b>  
          subprocess.     c>           TableEigenforms("       d>           ",  <  4  e>           ,   Ќ  Č  f>           ,       g>  
         ); quit; quit;  L  h>           echo '  , i>  
      	   ' | magma  , ( j>           System( L k>           )  D < l>                       m>           name     n>           Nstart     o>           Nstop   Ȱ  p>           k   x  p  q>           prec     r>           out t k.}   s>           N out; "f   t>           cmd     u>           s     "); quv>                w>                 x>              L        ,          |        H    y>  
         TableEigenforms  z>  B                                      0       <    W             $         l   &     %                                   |                  `                       L                        ,   	 <      8          |           l                `           V              	   	                
            4                       (         #   p       P   	   \                        
                   x                                       	          X  	             ,  !   8  #  H                          R  |  )                    l     
                            |            
      
    
                0     <   
     (       #    `      l    |                                  T                 H                        (             T        h  %    D  8  h  7     h   ,  8                  0  	 $                                  0 9    /                                                         D     P     \      h     t         -      /    ,                         8                            	                             T                         H  _        |   
          	 p  
      	                                                        @  	           4           \  	 (               P        
 
   D                      _                       
      
                    {>  0                                                %                                                                      $         (      c          |>           a    }>  
         f[%o] := [
 Ԭ ̬ ~>           f =   H >       >        >                                  T                     >           x  , $ >  
         <%o, %o, %o, [  p >           x-1   >           %o    >           ,    >           ]>  `~ X~ >           ,  z z >           
]; `y Xy >           
  xw pw >     0  4  8  <  @  D  H  L  P  T  X  \  `  d  h  l  p  t  x  >           name ;   >           N    >           k    >           prec   >           out  to the >           x    >  
         pdiv en(name, "a"); >           M    >           D    >           num H @ >           i  L D >           A     >  
         f  := Factor(D,i);  >           F f = ",f; n>           R  := Parent>           x  , $ >           p  t p >           p    >           a    >                >         >                                         H    >           TableCharpoly         ,	ʸ>                                       0    9 @              T   p      `   " 9 p   !                    @   $                                      % 9    $          	                                                  |   $         `      l   W            T                     5             5                                         P        8     D         %      ,     l      x                  	                 	       8          4     
   
      1                         	      h     $      
   X                L           1                                	      *     	                      
     F    $  H    0  J `@  E    ^ P  5        %      |             x       p  _                                                           `     	         (              D   	            8          P                        
           )                   `        |         $   	   `                                        >  (                                                                                                                   >           a  TZ PZ >        ?   //Table of characteristic polynomials of Hecke operators Tp on
 W >        <   //S_%o(Gamma_0(N)) for N between %o and %o and p between %o  V V >  
      	   and %o.

  n"   X >           charpoly%o := [*
  lP dP >  
         

// N=%o
 [*  T> >           %o  : : >           ,
  1 1 >           
 *] / / >           ,  , , >  
      	   		//p=%o
  $*  * >           
 *];  ' >                               >           name o 4o >           k TableCharp>           N1  k k >           N2  j |j >           p1  ,i $i >           p2  g g >           p  ` ` >           P  a a >           out [ [ >           N  N N >           M  L L >           S  0D ,D >           p  < < >                >                 >              L        d                  H    >           TableBSD \n ,	H,	,	ʸ>  ^                                      0       <    W             $         l      x          C       F       `                                                                   H         0     <            p   $     d              X       
      
                                       ' 9    &                                                         `      l   	           T         
            5           ( 5   $           X      5    .        ' 5    #      t  
        <      H   5 X        d  " 5            
 0                                                     Y          	                         ,   W         h           \             	 P                  	 x          <             8  x              W         $                      L        @  
      
      4                  >  H                                           $         (         ,      c             0         4         8         <         @         D         H         L         P         T         X      c             \         `      c          >           w    >        ;   // Table of ODD parts of BSD data for N between %o and %o.
 8 ( >        F   // [Level, Isogeny class, Dimension,Wq's, Order(0-oo), Torsion bound,
   >        9   //  L(1)/Omega, Modular Degree, cpbar...,ShaAnalytic].


  T L >  
          N1 := %o;
   >  
          N2 := %o;
   >  
      
   BSD := [*
    >           
Spawning level   H D >  
          subprocess.   >  
      
   TableBSD("    >           ",    >  
         ); quit; quit;  \  >           echo '  4  >  
      	   ' | magma   H  D  >           System( d  >           )   h  d  >           a       >           ,       >           a       >           *];
     >     h  l  p  t  x  |          >           name #  # >           N1 ableBSD(n>           N2    >  
         out en N1 and N2.}  >           N out; "BSD >           n    >           cmd , $ >           s       >                >         >              L                          H    >           TableBSD ];\,	H,	,	ʸ>                                        0        <     W               $         l   &     %                                   |                  `                       L                       ,   	 <      8          |           l                `           V                                 
            4                       (         *          P      \                       	      	     	        	 x  	        
      
 	     
! 1   
         
                 
@ 	     
/ 
   (  
1  8  
.      D  
4   P  
6     
3         
)                  
; 
     `      
)       |  5   
%    	     (    '           	     * 	     8      ,      7     0  )     @      	   L  $  \  #     l      	   x  +   *                          5 ,  
F          5 	     )      +    (                           0          H           5 X      	   d    t                     5            
            	     	                                	                    _        @      L              h               \      	 4  t                      	                  	       
    D                     0   <                     0  _        d     p         :       X           |       
      
                        >                                                                    c              >           a       >           [      // J_0(%o)
    |  >           %o  إ  ԥ  >           ,   x  l  >           
   `  X  >             ]    // end J_0(%o)

   >        "   [ ]    // J_0(%o)   (no newforms)
      >                               >           name      >           N       >           out me".}   >           x   P  L  >  
         pdiv n(name, "a"); B>           M       >           D       >           num P  D  >           i       >           A       >           p       >           p       >  
         dat = Factor(D,i);  >                >         >              L        \                   H     ?  
         TableBSDFull     ?  ^                                      0   %    <   % W   %         % $         l   &   x   '       '6       '9      & `         (      )      (          *      +     *          ,     ,       ,   H  ,       0  -   <  -       -   p  - $     d  .      .     . X       /
      /
    /        0      0      0               0' 9    0&          0      0                0             0            `  1    l  1 	     1     1 T         
    2       2# 5   2        2, 5   2(         3  X  3    5    22        3' 5    3#      t  2
        <  4    H  4 5 X  4      d  4" 5    4        4
 0         5      5      5     5                6    6       Y          7	      7     7           8   ,  8 W   8      h  8         \  9      9     9	 P       :      :     :	 x       7   <         0    8  x        =     = W   =      $  =           >      >   L  >      @  ?
      ?
     ? 4                  ?  H                                                             $      c             (         ,         0         4         8         <         @         D         H         L         P      c             T         X      c          ?           w     ܊  ?        .   // Table of BSD data for N between %o and %o.
  t  ?        F   // [Level, Isogeny class, Dimension,Wq's, Order(0-oo), Torsion bound,
  p  ?        9   //  L(1)/Omega, Modular Degree, cpbar...,ShaAnalytic].


       ?  
          N1 := %o;
 X  T  ?  
          N2 := %o;
   x  	?  
      
   BSD := [*
  |~  x~  
?           
Spawning level  v  v  v  ?  
          subprocess. u  u  ?  
         TableBSDFull("   t  ?           ",  xW Ph ?  
         ); quit; quit;  0 ?           echo '  V ?  
      	   ' | magma  | | ?           System( | ?           )  Tv Lv ?           a  $q  q ?           ,  Ho Do ?           a  k |k ?           *];
   ?     `  d  h  l  p  t  x  |      ?           name     ?           N1 ableBSDFu?           N2      ?  
         out en N1 and N2.}  ?           N out; "BSD ?           n   x{  p{  ?           cmd wning le?           s     ?                !?         "?              L                          H    #?           TableBSDFull .-	/-	-	ʸ$?                                        0   D    <   D W   D         D $         l   E&     E%          E      E     E         E     |              E    `           E            0  E            F      F 8    F      `  F         P  G     G        G D          H V   H      L  H t          I      I     I
          J    J                   K     K       K*     K     4  L    @  L      L             h  M    t  M     M      `  M \  	        N      N 	     N! 1   N         N(    N$        N                 NF 	     N5 
   (  N7  8  N4      D  N:   P  N<     N9         N/                  NA 
     `      N/       |  5   N+    	     O     O    	     P# 	      P1      P%     P0        P"    	   ,  Q  <  Q    	   H  R$ X  R#      t  O           5   NL          S2 	     S&      S(    S%         S                  S-            S         5   S    	   $  T  4  T      P  T           5    T        N            U	     U	 t              V     V       V     V	         W  D  W       _           X      X     X       (  Y      Y      Y     t  X	   4         h  [      [     [	 \        \      \   	      L
    (         ^     ^       ^0     ^         _     _       _        $  a   0  a       a:      a     |  I     <     p  c
      c
     c d                  %?                                                                    c              &?           a    '?           [      // J_0(%o)
  P L (?           %o  p l )?           ,     *?           
  , ( +?             ]    // end J_0(%o)

  ,?        "   [ ]    // J_0(%o)   (no newforms)
    -?                               .?           name   /?           N    0?           out me".}  1?           x    2?  
         pdiv n(name, "a"); B3?           M    4?           D    5?           num   6?           i    7?           A    8?           p  x p 9?           p  @ 8 :?  
         dat = Factor(D,i);  ;?                <?         =?              L         H                  H    >?  
         TableLRatio ( $ ??                                        0   i    <   i W   i      x   i $         l   j      k      j `         l      m       m"       m%       m)      l          n      o     n         q      q     q       0  r    <  r      r             d  s    p  s 8    s        s X          t 1   t         t     t         u     u      u>       uA     u	       v	      \  t            @  x   L  x     x        x 4        |  y  V   y        y p          z	      z     z          {     {                  |     |      |.       |1     |	     <  }    H  }      }             p  ~ 	   |  ~     ~        ~ d  
   
      1                          ;      >     @    ?         :          
   4  .    @  0     -         &     (             5      P      &       l  5    "                                                        (                      _     	   P      \              x               l       D              	                            
      } 	   0          
  $      0      <    d        x  '   x  0  x    L  X                     5       8     	                     _                              4        H  &   H  /  H     (    \              h  4       7      	        z     t     r    $                                        @?  6                                                                               $         (         ,         0         4         8         <         @         D      A?           a  ,   B?        3   // Rational parts of special values of L-functions
   C?           // N = %o,  %o <= k <= %o
    D?        .   // [dimension, LRatio(1), LRatio(2), ... ].


   E?  
         LRatio := [*
   F?        #   []     // S_%o(%o)   (no newforms)
 0 $ G?           [      // S_%o(%o)
 p h H?           %o  x x I?           ,  s s J?           
  q q K?           ]%o  // end S_%o(%o)

  0n L?           ,  k k M?              k k N?        %   []%o     // S_%o(%o)   (no newforms)
  f O?           ,   d d P?              c xc Q?           
 *];  8` R?     L  P  T  X  \  `  d  h  l  p  t  x  |  S?           name   T?           N TableLRatiU?           k1  ` T V?           k2    W?           out t)  Я X?           k ntf   Y?  
         M n [k1..k2] do = [*Z?           D n", k, N; [?           num ̐ Ȑ \?           i   x ]?           A  x p ^?           j    _?           dat A := Fac`?                a?         b?              L                           H    c?           TablePrimeSplittings '	ʸ('	ʸd?  :                                      0       <    W             $         l      x          B       E       `                                                    
      
  (         $      0                     X  ' 9    &                 L  h                   t                                                          + 5 (  '      4  4 5 D  0       P    X`      5 p  :    	  |  ' 5    #        
       
           5           " 5            
                         @                           4  Y        h  	    t                       W                                  	                   	         \         h              L     X   W            @                      |       
      
                        e?  @                                       c                                                                                                             c                            c              f?           w  xU lU g?        :   // Table of splittings of J_0(p) for p between %o and %o.
  R R h?        *   // [Level, dimension 1, dimension 2, ...]
  XP \P i?           SPLITTING := [*
 N N N j?           
Spawning level  F LF DF k?  
          subprocess. E  E l?           TablePrimeSplittings("  ,C m?           ",  xA lA n?  
         ); quit; quit;  = o?           echo '  H; p?  
      	   ' | magma  P9 H9 q?           System( ʸr?           )  6 t6 s?           a  0 0 t?           ,  . . u?           a  * * v?           *];
 ( ( w?                         x?           name \  \ y?           P1  Z Z z?           P2  (Y  Y {?           out V V |?           p out; "SPLI}?           p  K K ~?           cmd wning le?           s  ; ; ?                ?         ?              L                   <  @      H    ?           TablePrimeSplittings '	ʸ?  n                                       0       <    W         |    $         l                 `                                        1                                   ,                 h               P     \               D       
      
      x              ?                       c          ?           a    ?           %o
   ?  
   $  (  ,  0  4  8      ?           name # # ?           p  T" L" ?  
         out (	`(	('	ʸ?           X  T P ?           D    ?  
         dims omposition(X); ?                ?         ?            L  L   P             H          H    ?           TableBSD %o\H(	x(	('	ʸ?  H      T         X         \         `         d         h         l      c             p         t         x         |                                                                     c                            c          ?           w  H @ ?        ;   // Table of ODD parts of BSD data for N between %o and %o.
 | x ?        F   // [Level, Isogeny class, Dimension,Wq's, Order(0-oo), Torsion bound,
  $  ?        9   //  L(1)/Omega, Modular Degree, cpbar...,ShaAnalytic].


   P  H  ?  
          N1 := %o;
     ?  
          N2 := %o;
 P  D  ?  
      
   BSD := [*
  D  8  ?           
Spawning level        ?  
          subprocess.   \  ?  
      
   TableBSD("      ?           ",  @  8  ?  
         ); quit; quit;    ?           echo '    ?  
      	   ' | magma       ?           System(   ?           )       ?           a       ?         ?           ,       ?           a   P  L  ?           *];
   X  ?                         ?           name  ( ?           N1 ableBSD(n?           N2  0
 (
 ?  
         out en N1 and N2.}  ?           N out; "BSD ?                ?           n   <  4  ?           cmd t  l  ?           s   X  T  ?           w   `  X  ?           TableCongruenceR 6(	&(	ʸ?         ?         ?              L        ,          P  T      H    ?  ^                                      0       <    W             $         l      x          C       F       `                                                                   H         0     <            p   $     d              X       
      
                                       ' 9    &                                                         `      l   	           T         
            5           ( 5   $           X      5    .        ' 5    #      t  
        <      H   5 X        d  " 5            
 0                                                     Y          	                         ,   W         h           \             	 P                  	 x          <             8  x              W         $                      L        @  
      
      4                  ?  F                                                         c                                                                                                               c             $         (      c              ?        "   // Table of congruence numbers r.
      ?  
      
   N1 := %o;
      ?                ?        +   // [Level, Isogeny class, r, structure].


     ?  
      
   N2 := %o;
  `  \  ?           CongruenceR := [*
  8  4  ?           
Spawning level    ȶ  Ķ  ?  
          subprocess.     ?           TableCongruenceR("  ĳ    ?                ?           ",      ?           echo '    ?  
         ); quit; quit;  @  ?                ?  
      	   ' | magma       !@                ?           System(   ?  
         out ile "name".}   ?  F                                      0       <    W         x    $         l                `                                                                                       0          $             X         L   
       
  \    @     t                                                                h                                                      	  @        L   ' 5 \   #    
  h   0 5 x   ,         	   X  	     5    6        	 ' 5    	 #         
 4         
       
  5   
         
 " 5    
       P  
 
        8       D             t    ,                  D        h  Y           	                               W                                    4   	      (                	                                            W              t                                 
       
                     ?           )       ?           a       ?           ,       ?           a   x  p  ?           *];
     ?     0  4  8  <  @  D  H  L      ?           name      ?           N1      ?           N2  D  <  ?           out     ?           N out; "Cong?           n       ?           cmd wning le?           s   H  @  ?            `  L   d  
           \          H    ?           TableCongruenceR X(	&(	ʸ?  ^                                      0        <     W               $         l       x            	         8                `                                           V                       $       0         
                     @           t                 *   t    h                                       !       !      !         !            " !   $  " +   4  " +      @  " -   L  " 4    X  " C Q h  " B     x  " 7    E   " 3        " -        " - a   "          "           " 	        0  "     	        #       #       #       #              P  #    
   
      $ 	     $ 	 D            t  %      %  
      %      % 	 h        &     &        _          '       '      '          (       (       (      D  ' 	            8  *       *    `  * 	 ,        +       +  T          
             -      -        - 0     -          .      .        _          0       0        0 :      0      L      L       @  2 
 	     2 
     2  4                  ?  "      h         l                 V   p         t         x         |                        c              ?           a   h  d  ?           [      // J_0(%o)
  	 |	 ?                          ?           %o    ?           ,    ?           
    ?             ]    // end J_0(%o)

 8 ?        "   [ ]    // J_0(%o)   (no newforms)
    ?                           ?           name   p  ?           N       ?  
         M  Open(name, "a"); ?           D  p d ?           num    ?           i    ?           A    ?  
         r  := Factor(D,i);  ?           struc  < ?           dat 2.5*Heck?              L                          H    ?  
         TableConnected 		?  Z                                       0   =     <   =  W   =         =  $         l   >    x   >        > %       > (       ? $       ? & b   ? #         ? ,     ? )         ? 8       ? ?     ? 1            ? 1           <  >  `      0  @ 
      @ 
     @  $                  ?                                 c              ?           a    ?           C[%o,%o] := %o;
    ?                 ?           name  4 ?           N    ?           k     ?           out < 4 ?         ?              L         P                  H    ?  
         TableConnected  t ?  l                                      0   H     <   H  W   H          H  $         l   I    x   J        K        K 
       K        K       I  `         L       L      L           M       M        M    8  M           N    ,  N        N    l  N       T  O    `  O        O      O  H       P      P        P      P  |       Q      Q       Q <       Q @     Q         R 
      R 
    R       $  S     0  S       S              X  S ) 9    S (          S       S  L  h             S       t       S               T       T       T           	     T +     T *    	      T       T                 T  	             T        <  	  |  U 	      U  
    U       U        U "     U 	 p             V        V ( 5   V $        V 1 5   V -         W $ X$  W #    5 4  V 7      @  W + 5 P  W '       \  X $ Xl  X #    5 |  W /        X + 5    X '        V    
       Y  
     Y  5   Y         Y % 5    Y !      (  Y           Z       Z       Z    L  Z 	                [      [      @  Y         T 
    T        S       h               @  @                                                                            c             $         (         ,         0         4         8         <         @         D         H         L          @           w    @        B   // Table of connected in the box %o <= N <= %o and %o <= k <= %o.
    @        ,   // C[N,k] := either 1 (true) or 0 (false),

    @  
          N1 := %o;
   @  
          N2 := %o;
   @  
          k1 := %o;
   @  
          k2 := %o;
   @        '    C := RMatrixSpace(Integers(),%o,%o);

  	@  
         
Spawning ( Ħ  
@           ,    @  
         ) subprocess.  x @           TableConnected("    @           ",   ؠ @           ,    @  
         ); quit; quit;   @           echo '   @  
      	   ' | magma    @           System(  @           )  ̑ đ @     T  X  \  `  d  h  l  p  t  x  |        @           name ; ectio@           N1 ableConne@           N2    @           k1    @           k2  , $ @           out ) and k1@           N out; " C :@           n     @           k    @           k  x t @           cmd Spawning @           s  4 , "@                 #@                                            H    $@  
      	   Conductor     4˸%@  @                                       0   r 2     r 1       L   r    X   r      r          r      @              r     $   h        r               r         r 
     	    r                 &@             '@           N sic;   (@           p    )@                *@                                            H    +@           OddPart eger,@  B                                       0   x 
    <   x      x           x      d   x    p   x #     |   x /      x 1     x .        x $        x !        x  L   X        x          	    x  $               -@       .@           n  L H /@                0@             8                              H    1@           DotProd  sel2@  X                                     0   ~      <   ~ * P L   ~ )     \   ~ "         ~                  ~        ~      ~           ~        ~      ~         ~          ~      x              ~     $        (  ~           )    ~ 
     	    ~                3@           4@           a  s s 5@           b  r r 6@           i  l l 7@                8@             \                           H    9@           Volume  e :@                                        0       <      L        y               $         |    " R      ,                              /     "                                     S        2               p             .   D    R  T          `   " , p         |   $       %      $          $       	     8              )    ,          	           $               	                                P    P                    D                  8  `              |  6                                                   	                        <    R  L   !       X   % L h         t   '       (      '          '       0                    B          	                        ;@                                      <@                     =@           L  d d >@           n   a a ?@  
         B gree(L[1]); } atti@@           b  R R A@           VB  V V B@           r VectorSpacC@           b  L L D@           Mat  0; G E@                F@                $    (        0         H    G@           Norm < P< H@  >                                      0          <    (  L    '     \           h    +     t    ,       +          +         =      <         5    c         	      $                   I@                J@     , K@           x  ; ; L@                M@           < 0   @    T       8 `         H    N@           ToNth  tant(O@                                               T            $             h         H    `                                                                  	     	                                           D             	     	 8     `      l                                |         	     	                                  X            ' 5     #     	     	          T                (  0    x    |      H                     P@     c             D     c             H     c             L     c             P         Q@           1st :  + R@           2nd ( ( S@           3rd (' $' T@           th  X$ T$ U@     X \     V@           n  L/ D/ W@  
         --temp--         X@                Y@           l            p       h          H    Z@  
         PrimeSeq nte8l 	xl 	[@  >                                       0        <                        d    ' 9     &                  
 X   t                   $            
          	                     \@     t x | ]@           p1  $   ^@           p2    _@           p    `@                a@            0                        H    b@           BaseExtendCharacter `l 	ʸme(p)]; c@                                              P    	     $                       D              h                   %         )       -        ,      (          $                                   $             0       <     L         \                                               h                                  	      	                t                 
 	                        d@                 m         m                    m         m          e@        f@           eps   g@           F  l d h@           i    i@                j@            0                        H    k@  
         BaseExtendMlist   l@  @                                            P         $                        D      t                               h                                  
 	                         m@  
               c          n@           o@           mlist     p@           F       q@                r@            P   
                    H    s@           BaseExtendQuot 	8 	8f 	ʸt@                                      <    (     H    ,    0    1    T    0  d    +          '                                                                                                                    "    $                      p        4                     d                                                                   %       $      +  $   *    y 4       ,                      p   -     |   1   d   6       5     0          ,                                                        "     !      (                                       '    X  4               P           h  	      
      
                  D              
 	                    u@  "      h                    h         h         j         j         j                    j         j          v@          w@           quot     x@           F       y@           i       z@           V   \  X  {@           i       |@                }@            0                         H    ~@           BaseExtendDecomposition   @                                            	        $                      @             @        =   BaseExtendDecomposition: not yet programmed, though not hard!   |  @           @           D sic;    @           F       @                @                $    (        <         H    @  
      
   BaseExtend      @  V                                      0     ( @    
       L     ( \         l                              ' A     &           -      *                            	           8    $                        & 1 (   %    ,           x             X   ) 2 h   (    >     "          L                                                                                   ,                  h                 \      D                     P                    |                             $                   "      $       #       ) d    !     D                            8      t    	  \                     h  
        T                                         !      #        "       * e          <                             0                          l                          "       !       ( f                                          ,    x               
 	                         @  6                        3          3                                                                                                                              @     , 0 4 8     @           M sic; in [1@           F   4  ,  @           V rn M;   @           N  := Vector@                C                       L                          B                       L                         {F                       L               
          F              F        F                       L               @ <         F              F        F        }            F                       L                         F              F              B                       L               
 
         B                       L               
 
         ~F        O      aF        B        n                              <                      P          B                       B                 @    	C  T                                                                         J J  @ pK pK   J J \K \K  K  K J K I I `J `J J J $K $K J J J J 4K 4K XK XK J J K K K K LJ LJ I I xJ xJ PJ PJ K K J B  "           <  (                                                                                                   B                   @                B             @      B                 @˸B  
                @	     @  
         HeckeBugWatch ******@  
         HeckeVerbose        @           HeckeSuperverbose           @  
         CManSymList ********@  
      	   CQuotient **********@           ModSym ey ar@  
      	   ModSymFac           @  
         GetCategory ,{ خ @  
         SetCategory gory;   @  
         NormalizePair //////@  
         P1Reduce , m0QhQ@  
         EnumerateP1 c L @  
         ManinSymbolList ////@           UnwindManinSymbol     ˸@  
         WindManinSymbol ener@  
         __sig__0 ʸ@  
         __sig__1 { `  @  
         __sig__2  s];  " @  
         Sparse2Quotient  ˸@  
         Pivots   or lt Tr @  
      	   Quotient2     @  
         Quotient ; s, j);  @           ManSym2termQuotient  	ʸ@           ManSym3termQuotient   	ʸc,n,K); @  
         __sig__3 0); s.} ˸@  
         __sig__4 0); s.} ˸@  
         __sig__5 sign); ] @  
         __sig__6 k,sign);  @  
         __sig__7  i 2 @  
         __sig__8 " " p" @  
         TrivialSpace # $ @  
         __sig__9  | @ @  
      	   __sig__10  X^ T^ @  
      	   __sig__11    @  
      	   __sig__12    @  
      	   __sig__13  i @j @  
      	   __sig__14  z  { @  
      	   __sig__15  d c @  
      	   __sig__16  H  @  
      	   __sig__17  d  @  
      	   __sig__18  g   @  
      	   __sig__19    @  
      	   __sig__20    @  
      	   __sig__21  (  @  
      	   __sig__22    @  
      	   __sig__23          @  
      	   __sig__24   ~ @  
      	   __sig__25  ,  0 @  
      	   __sig__26  h f @  
      	   __sig__27  8" ؒ @  
      	   __sig__28  \  @  
      	   __sig__29  { @ @  
      	   __sig__30  _ _ @           idxG0  |^ @  
      	   __sig__31    @  
      	   __sig__32 ]);  ; @  
      	   __sig__33  j k @  
      	   __sig__34  [ Z @        	   CFastData acW	W	@@	ʸ@  
      	   __sig__35  ~ ~ @  
      	   __sig__36  Z Z @  
      	   __sig__37   4 @        	   __sig__38 t)*VEinv);  H @  
      	   __sig__39   ع @  
      	   __sig__40    @  
      	   __sig__41  |\ \ @  
      	   __sig__42 t];  `+ @  
      	   __sig__43  $ <% @           ActionOnModularSymbolsBasis ********@  
      	   __sig__44      q @  
      	   __sig__45 M); 	p	@  
      	   __sig__46         @  
      	   __sig__47      @  
      	   __sig__48 	xR	   @  
      	   __sig__49 	`	   @        	   __sig__50 B]]; 	`		ʸ@        	   __sig__51 Basis(K),B)); @( @  
      	   __sig__52  l ( @  
      	   __sig__53   H @        	   __sig__54 larSymbols(M));  @  
      	   __sig__55 gr		@  
      
   ReduceCusp /////////@  
      	   CuspEquiv s(	ȇ	@           CuspToFreeHelper    `7 @  
      	   __sig__56 [a].      @  
         LiftToCosetRep      @  
      	   __sig__57  P  @  
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      	   __sig__63    @  
      	   __sig__64  Z Z @  
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      	   __sig__82   h A  
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   convergent 	    0˸
A  
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      	   __sig__91 2][2],M); A  
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         alphabet    A  
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   __sig__111 asis(K),B));  %A        
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         DefaultPrec &  A           Int1  ; 8 A           Int2 rn h A        
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   __sig__255  " " A  
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   __sig__268    A           ComputeSpecialValueAndRankWt2  $ A  
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   __sig__271  xj i A           mu0 ********A  
         mu20 zation(n)]);  A  
         mu30 rn rn t# `$ A  
         c0 turn rn r* * A           g0 turn egerA           mu1 ; gers()A  
         mu21 eturn   ) A           mu31  hen reA           c1 n; hen reA  
         g1 turn rn  ^ ] A           ss0 ; gers()A           muXNp n )  )A           mu2XNp  \ A           mu3XNp  l A           cXNp ( |( A           gXNp  (n);  A           ss1 ; - mu3XA           eisen (n,p) A           S0 n; rator(A           S1 n; *c0(n)A           idxG1 ers()|A  
      
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   __sig__279  @V W A  
      
   __sig__280  4 3 A  
      
   __sig__281  < ( A  
      
   __sig__282  D  A  
      
   __sig__283  
 L
 A  
      
   __sig__284 lex:=alloA  
      
   __sig__285    A  
      
   __sig__286     A  
      
   __sig__287  d  A  
      
   __sig__288   H A  
      
   __sig__289    A  
      
   __sig__290  ( 4 A  
      
   __sig__291  Ԝ ؜ A  
      
   __sig__292     B  
      
   __sig__293   h B  
      
   __sig__294  L  B           AllStandardCharacters  < B  
      
   __sig__295  @  B  
      
   __sig__296   & & B  
      
   __sig__297  1 1 B  
      
   __sig__298  6 6 B           MonomialsOfDegreeD_recurse  87 D7 B  
      
   __sig__299 Ring(Rati	B  
      
   __sig__300  (1 $1 
B        
   __sig__301  b in r];  , B  
         CohenOesterle +	4-	B  
      
   __sig__302   9 B  
      
   __sig__303    B  
      
   __sig__304  [ Z B  
      
   __sig__305  T  B           mumu   B  
      
   __sig__306 ) : M in B  
      
   __sig__307 M)) : M iB  
      
   __sig__308    B  
         SSTABLE  >); DimensiB  
      
   __sig__309  @ @ B           R sic;  ? B           x  B B B           j  T P B           PHI lynomialB        
   __sig__310  : a in fac];  B  
      
   __sig__311  0 , B  
      
   __sig__312  H @ B  
      
   __sig__313  H~ @~ B  
      
   __sig__314  x x B  
      
   __sig__315  X L  B  
      
   __sig__316     !B  
      
   __sig__317   | "B  
      
   __sig__318  e e #B  
      
   __sig__319  $L  L $B  
      
   __sig__320      %B  
      
   __sig__321 	P&	ʸ&B  
      
   __sig__322 l(p))];  'B  
      
   __sig__323  p  l  (B           SerreModPQHelper &	x~&	ʸ   P  )B  
      
   __sig__324      *B  
      
   __sig__325  pB lB +B  
      
   __sig__326  03 (3 ,B  
      
   __sig__327  T  L  -B  
      
   __sig__328 ), M;   .B           ToLatex @  /B  
      
   __sig__329  p p 0B        
   __sig__330 	0K%	ʸrn 	ʸ1B  
      
   __sig__331 ), M; ! 2B  
         EVIDENCE_CURVES ****3B  
      
   __sig__332      4B  
      
   __sig__333  ̽  Ľ  5B  
      
   __sig__334      6B  
      
   __sig__335    7B  
      
   __sig__336  0q $q 8B  
      
   __sig__337  % % 9B  
      
   __sig__338      :B  
      
   __sig__339  t  p  ;B  
      
   __sig__340    <B  
      
   __sig__341  t p =B  
      
   __sig__342  8^ 4^ >B  
      
   __sig__343  % % ?B  
      
   __sig__344  @ 4 @B  
      
   __sig__345  H  D  AB  
      
   __sig__346      BB  
      
   __sig__347  \ T CB  
      
   __sig__348  < 0 DB  
      
   __sig__349    EB  
      
   __sig__350 )];   FB  
      
   __sig__351 ; } } GB  
      
   __sig__352  |f xf HB  
      
   __sig__353  = = IB  
      
   __sig__354 us(ParentJB  
      
   __sig__355  L  H  KB  
      
   __sig__356     LB  
      
   __sig__357  p  t  MB  
      
   __sig__358      NB  
      
   __sig__359      OB  
      
   __sig__360 :  thougPB  
      
   __sig__361    B  *                                     0   !    @   !       L   !      X   !    h   !          !       !  $           ! &      ! &         ! (       ! )      ! (         ! (     !               "     "         "       X  "           8  #   H  #         #         #  ,        x  $       $  	    $         $  l          % 	      %       %       D  %            &       &       &      &     
    & 	         '  	    '  (      &    4         h  )     t  )     )          ) $    )          )         )  \          *       *     *          *     *          *         * %  0  * #       <  * -  L  * )      h  *               t  * 2      * 9    * 5         * <      * C    * ?        * 1               *       |  *    	       + 
      + 
     +  	   (  +     4  +   D  +        P  +   `  +       p  +          +  	    +                    B           No solution exists. Ta  ta  B      
 	 	 	 	 	 	 	 	 	     B  
         a sic; *t + c0); iv B           b   F  F  ~B  
         a0 ntResElt    ˸}B  
         b0  4  L  d  |  |B           m1      {B           m2      zB           t haracterisyB           c0      xB           R rn "No solwB           c1 sidueClasvB            H  uB           	 t   	    	 
      	 	         
 
 tB           ChineseRemainderTheorem   sB  *                                     0   0    @   0       L   0      X   0    h   0          0       0  $           0 &      0 &         0 (       0 )      0 (         0 (     0               1     1         1       X  1           8  2   H  2         2         2  ,        x  3       3  	    3         3  l          4 	      4       4       D  4            5       5       5      5     
    5 	         6  	    6  (      5    4         h  8     t  8     8          8 $    8          8         8  \          9       9     9          9     9          9         9 %  0  9 #       <  9 -  L  9 )      h  9               t  9 2      9 9    9 5         9 <      9 C    9 ?        9 1               9       |  9    	       : 
      : 
     :  	   (  :     4  :   D  :        P  :   `  :       p  :          :  	    :                    rB                              	                    qB           No solution exists.     pB     	 	 	 	 	 	 	 	 	 	     oB  
         a sic; *t + c0); iv nB           b   D  H  mB           a0        lB           b0      kB           m1  H  L  jB           m2  \l  tl  iB           t odulus(ParhB           c0  d^  ^  gB           R rn "No solfB           c1 sidueClaseB            W  dB           	 L           	       	 x	         
 
 cB           ChineseRemainderTheorem  v  Dv  lv  bB                                        0   ? "     <   ? $     ? !     	    ?  $                   aB     	 |	     `B  
         a sic; *t + c0); iv _B           b   HZ  `Z  ^B             ]B           l	 L           h	       p	 X	         
 
 \B           ChineseRemainderTheorem ʸa); f a [B  R                                       0   D    <   D 
     D 	         D  $        l   E      x   E      E          E                 F $        F &       F (     F '        F #         F 	           E     `            H 
 	    H                ZB     d	 `	 \	 YB           A   U  V  XB           c the list AWB           i 1]; e ChinVB                UB           L	            H	       P	           
 
 TB  
         IsSquareFree h  h  SB  D                                       0   M /     M .       L   M    X   M   h   M       t   M      M          M      @              M     $           M               M 
     	    M                     RB     @ \     @           n   k  k  A           q   O  O  (            X\<           h  @           H        l            
 
 [<  
         SquareFreeRoot    Z<                                         0   R      R         R  $          `   S     S       |   T ,       T 0     T /         T +                T        T       T      T 
          T        T      T     T       (  T !   8  T         T          S                    T &    p   H      S       d    |  S        S        S         U =      U A    U @         U <               U     $  U    0  U   @  U        L  U #    X  U (   d  U +  t  U '        U 2    U .        U !         U                   U 7             U             U         U     	    S  T               R<     D  <  ,  (      Q<           N sic;  q[2]O<           fact f  4g  K<           i       J<           i   pi  i  C<                A<             4                    `          
 
 ?<  
         Subsequences h  h  3<                                        0   Z      <   Z   L   Z 	         Z     `      l   Z     x   Z      Z          Z               [                 [                 [ "         [       [     [         [       [  	    [       t  Z  $   $        X  ^ "     d  ^ %     ^ !             ^           ^ )     ^           ]        ]       ]                   ]              ]               ]                   ^     L      d  ]        0      ]      	    ]  H                  1<           h      /<           n sic; ers()%<           r   v   v  #<           I Sort([ [ i<           i        <                <                               0            
 
 <           Choose  T  <  n                                      0   c     <   c      c 	         d                 d                   d #     d "         d    h   d      d          d    L   d  	    d            f        f "     f           f       f                   f        $       f        @  	    f  X       c  $      t                  <           ;           S   Ѝ  ԍ  ;           r      (  ;           X       ;            A ;             P                              
 
 ;           Subsequences      (      ;                                        0   l      <   l   L   l      \   l 	         l     p      |   l        l      l          l               m                m                   m #     m "        m       m   (  m       4  m       m  	    m       t  l  $   @          t  p     p          p      p           o        o       o      o          o                   o              o               o 
                  p     h  $       o 
       @  	    o  X                  ;                  ;           S sic;    ;           r   ԉ  ؉  ;           I   X  `  ;           i       ;               ;             L           d         p         
 
 ;           Choose equen(                                         0   u     <   u      u      	    u  $                   E     h l     E           S   l  t  E           r   Ȍ  Ќ  E            PE           | @                  x          
 
 E           Factor  H  E                                         0   z      z      	    z  $               E           x   ȋ  ̋  E            PE            P                            
 
 E  
         Factorization n(x); E  h                                       0    "  @    !               x    $          p    "      !     L              @        -       /      .           3       5      4         2          ,                *                    ;           h   *       4        &     	      d               E        E           f         E           D ctorizatioE           P   ȋ  ̋  E            L E            P                            
 
 E  
         Factorization       E                                         0       @                        $          p    "      !                   d                            
                                   
                 4    $       0   "  @   !       L   '   X   )  h   (     x   &                                             /                                 	                         E          E           x sic; rizatE           N eqEnum ereE           D   ,  4  E           P   \  `  E           P       E            EVIDE            L                        
 
 E           Primes  P inE              E        \
         rimeC        E      C           /home/was/magma/Hecke/hecke.m       B                                  <        8 $         B  .         $                 o        %       p        L     m        
     q        (     r                        $     s          B                B              B        9      ʸB     , 
    C              `UU   B     x
 l
     B                     B                          $     $       
 
         B                       L               
 (                 E                       L                
         `F                       L                         |F        }F                       L                         F        =      F        F                       L                         F                       L               8 4         F              F                       L               D @         F        g      F        F                       L               P L         F        !      F        F        '      B                B                      E      B                       L               
 
         yF        B        !      F        B                       L               0 4                 E        
         KoheE        	         at B  
         BalancedMod        bF        	         KohecF        t	         at  B           x Matrix  t B           n er_genera B        t
 `                B        .   /home/was/magma/Kohel/elementary_arithmetic.mg  $   B  :      5   3  
   3   (             Y  6  $                   7  &          /      t  8  s    c    n   ,  .                       ]  A          >     F                       L               , (         F              F        F                       L               \ X         F        M      F        F                       L               h d         F        9      F        F                       L               t p         F              F        F        5      F                H                       L               # #         H     %         B               /H              .H        1H        4H        H              H              H                F        F                       L                         F        +      F        F                       L                         F        3      F        F                       L                         F        	          F                       L                |         F        F                       L                         F        =      F        F                       L                         F        7      F        F                       L                         F        !      F        F                       L                         F     %         F        F                       L                         F        '      F        F                       L                          F              F        F        ?      F        B           p
 L           d
       |
 `
         
 
 B  Z                                       0        <           
          $         l         x                                                                                              	           <    `                 
 	      0                  B           T
 t   P
    H
 
      X
 
         
 
 B           ChineseRemainderTheorem ʸrn ʸB  *                                     0       @          L         X       h                      $            &       &          (        )       (          (                                         X             8   2  H   1         *           ,        x           	               l           	                    D                                       
     	           	      (          4         h       t                  $                         \                                                         %  0   #       <   -  L   )      h                 t   2       9     5          <       C     ?         1                      |      	        
       
       	   (       4     D          P     `         p              	                        B                              L
                    B           No solution exists. k  Dl  B     D
 @
 <
 8
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 ,
 (
 $
  
     B           a   >      B           b   @?      B           a0      B           b0  R      B           m1        B           m2      k  B  
         t (Parent(b));  Ј  B           c0      B           R rn "No solB           c1        B           
 t   
    
 
      
 	         
 
 B           ChineseRemainderTheorem   ؃     B                              
                            C           3             c      d      e      C           f      g      h      i      j      C        T              C                      C        0              C        D  \        C     X   T     C        l  d        C     X   T     C          l        C  
   X   `        D         C        Ĥ              C                      C          |        C  
   X   p     X   X          C                      !C        إ              "C                      #C        t              'C        h          %C                  &C     X        (C     X        *C                  D        $C        Ȧ          )C  
              X            +C     X        ,C        h              -C                      .C                      /C                      0C                      1C                      5C        ة              3C           	       4C                          X        X   h     X        X                  X   P        H     6C                      8C                     E      2C                  7C        H               X   P     9C        ,              :C        H          ;C     X   L                         <C        l              =C                      >C                      ?C                      @C        ܪ              AC                      BC                      CC        ̫              DC                      EC        H              FC        d              GC                      HC          $        IC                JC                      KC        t              LC                      D     X   4             NC        ĭ  <        OC     X   4     PC                      QC                      RC        <              SC           6      k      l      TC          T        UC  
   X           L         VC                      WC        خ              XC                      YC        D              ZC        d              [C                      \C                      ]C        ܯ              ^C                      _C        8          `C     X   L               X   x     aC        x          bC     X   x     cC                      dC                      eC                      fC                      gC        ,              hC        T              iC        x              jC                      kC                      lC        б              mC                      nC                  oC     X        pC                  qC  
   X        X            rC                  sC     X        C     X   p             uC                  vC  
   X   p     X            wC                      xC                  yC                zC        г              {C                      |C                  }C     X   L                         ~C        <              C        `              C                  C     X   4     C        ܴ              C                      C        d          C     X        C                      C                      C                      C        4              C        P              C        p              C                      C                      C        ж              C                      C        \              C        t              C                      C                      C        P  T        tC                      C                      C          `        C  
   X   p     X            C          h        C     X   \     C                      C        <              C        X              C        |  |        C     X   X     C                      C                  C     X        C        L              C        p          C     X        C                      C                      C                      C                       C  "      0                      T                         U   "         Y?       2x@2x           C  j                H         t                 X                  <         h                  L         x                 \  	                @         l                  P         |                 `  
                D         p                  T                  8          d                                       !                           C                    	                                 
                                   C  "      0                      T                         U   "         Y[      2x@2x           C  j                         л                                            Ļ  	                         Ի                                             Ȼ  
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 /                                     C        x         C     0        C                  C     0        C                      C               C                                     %   )   +   /   5   ;   =   C   G   I   O   S   Y   a   e   g   k   m   q                                                                                         %  3  7  9  =  K  Q  [  ]  a  g  o  u  {                                              	      #  -  3  9    A  K  Q  W    _    i  k  w                                                  )    5  7  ;  =  G  $  Y  &  _  m  q  s  w                              :      ;    	        %  '  C  ?  C  F  I  O  U  ]  c  i                                        	            '  )  /  Q  W  ]  e  w                                                    #  +  /  =  A  G  I  M  S  U  [  e  y                                             '  7    K  O  Q  U  W  a  m  s  y                        %            -        *   ,   0   2   <   H   J   Z   \   b   f   6  r   z   <           B     D     G           I              &  ,  .  4  8  >  L  R  V  X  ^  b  h  t  z                                     (  *  :  B  F  R  `  j  l  p  x  ~                                                  $  ,  2  6  H  P  Z  `  f  n  x                                          8  :  J  d  h  '  v  |            /    1      3               
        (  *  4  A  F  H  X  ^  r                                                 &  *  0  8  >  D  T  `  b  f  t  z  ~                                         .  2  :  L  P  V  X  \  b  d  p  t                                       !   1   3   7   	  K     Q   c   {                                      "            *      '  0  ?  2  W  Y  k  q  7  9              ?                        /  1  5  ;  =  C  I  S  Y  e  q                                      +  9  ?  I  U  W  [  a  i  o  y  {                                          -  3  A  E  M  W  _  k  }                                  #    1  7  ;  =  I  O  S  U  [  q  (  y  }  )    +        .              	      !  %  '  >  -  7  E  K  O  W  a  g  {  J                                      	      !  5  9  E  S  o  u                                          "   .   8   P   R   V   ^   d   h   p                                                                     0  6  
  N  `  d  l  v                    !  #               ,  2  <  >  H  J  P  Z  h  4  8        =        @            H          K     >  @  J  L  R  V  \  b  j  p  t                            
    $  .  4  B  F  H  N  X  `  f  j  p                            $  6  <  >  P  T  Z  \  f  n  x  ~                                            "    .  2  @  F  J  X  d  h  j      ,                    5    
        (  *  6  T  E  f  l                            L  M  N  O  #   P  ?   A   Q  M   R  W   S  T  u   U     V  W        X  Y              Z  [          #  1  \  ]  e  m  s  }  ^          _  `    a  b      c    d  e  f      g  '  h  i  ?  E  j  O  U  ]  o  s  k  l        m  n    o    p        q  	      '  -  /  K  M  S  r  s  t  u  u  }    v    w  x  y  z  {            |        )  /  ;  =  }  a  e  g  q  ~                                            %  +      K    a  g  o  s                                  )    3  9      Y  _  c  o  w  }                                               9       =          ]                            \         :      C           }         ]         ;       G            <       I          i                    ~         ^               O                    _       %  =       S                                      `               Y                                                           3  >      a                   	  a      7  ?        b       9  @      g                         =  A       k                  m                                   q                                                      c       K  B                                         #  d      Q  C                                                                             -  e      [  D                 ]  E         !                3  f       a  F                                       9  g       g  G         "                  #                                 A  i       o  H          $                                       u  I          %               K  j                  &      {  J                        Q  k         K          '                        )        W  l        L         (                  )                                _  n         M                5         	          N         *                  +      ;        i  p       =           ,         O          -                                                         G                    P       w  r         Q         S         T       ;  h         Y       Y  m       e          e  o       k  q          3         y         |                                  +         7         U         Y         _         q         s         C        $             C        L            C                      C                     C        Ⱦ          c  C                      C                      C                  )C        8            C        X             C        x             C                    C          L      C  
   X   L                   C        ̿              C                      C          \      C  
             X   P       C        P          C        |  h       C               X   P                          C          p        C     X   L                         X   P         C        (          Q   C        @  |      C     X   L               X   d     C        `          C  
   X   L               =   C                  C                  T   C                      C                  C                     C        <          7  C        x          C                     C                      C                  C        d      Y   C     X   L                         C                  a   C                  C        8              C        X          =  C        x              C                     C                  [  C                  C                  ]   C        8          M  C        T          C        t          ^   C                  U  C                      C                  .  C                  s  C        8            D               D        X              D        x              D                      D                  1  D                      D                      D        <             D        T  $       	D  
   X   L                   
D                      D                      D        $          d   D        \            D        x          D                     D          D        D     X   <     D                      D        \              D                    D                    D                     D                      D        0  d    D               D                      D                      D        @              D        X  x    9  D                D                      D                      !D              m   "D                #D        0             $D        `          %D                      &D                     'D                       (D        D          q   )D        h        *D               +D                      ,D                      -D                       .D        D              /D        h          ?  0D                    1D                  2D               3D        ,          u   4D        D            5D                    6D                      7D                    8D                    9D        8             :D        \          %  ;D                      <D                      =D                      >D        h            ?D                   @D  
   X   L                 AD                  BD  
   X   L               CD                  |   DD                      ED        L          FD                      GD                      HD                      ID                      JD        `  ,    Q  KD  
              X   $        LD                       MD          8        ND  
              X   $     ]  OD                      PD          D       QD     X   <     RD        4          g  SD                      TD                     UD                  o  VD                    WD        $  `    K  XD     X   L               X   <                   YD                     ZD                    [D          p        \D               ]D        8  x       ^D               _D                    `D                      aD                     bD                     cD        X          dD                eD                    fD  
        gēǰ}?    mD  
        gēǰ}?Ѹ!;hD  
         4h!b܀jD  
         4h!b܀gD                  kD               iD                  lD                 nD     X        qD        4              pD        T         oD     X        rD                    sD                  tD        |          zuD                  0˸vD        p      _twD     X        xD        $      yD     X        zD        <          {D        \      *  |D                }D        L      g  ~D     X        D        d              D                  D     X        D                  %   D                  D     X        D                  /  D        \          /   D                  D           $    0  D     X        D          ,        D  
   X        X            D        P              D        p  8      D  
                            D        (  @    D     X        D        D              D          L    O   D     X        D        0          D        l             D          \    Y   D     V                   X   T     D          d        D     V                   X   T     D        $  l        D     V                   X   T     D        \  t    m   D     V        D          |    D               D                   D     X        D        8            D        T          D     X   x     D                  ;  D                    D                  D                      D                D     X        X        X        X            D                 D     X        D        0          D     X        D        H         D     X        D        `         D     X        D                D     X        X        X        X           D                  D     X        D                  D  
   X        X          D                     D                  
  D                  D     X        D        (        D     X        X        X        X        X        D        D         D  
   X        X            D        `             D        x      D     X        X        X        X            D              D     X        X        X        D                 MC                    D                    D                  o      p      m      q      r            s          D        x            D                  -  D                      D                     D                    D                   D                  J  D        8          #  D        `              D          P        D        $     D                  G  D                      D        <          L  D        T  d      D        $     D                      D                      D                  %  D                  D                      D        <          G  D                  D                D        $     D        T          7  D                D     X        D                 D     X        D                     D        (          D        X          S  D              e  D     X        D                  D                  U  D        (            D                  D     X        X   4     X        D                  V  D              a  D     X        D                      D                     D        @        D     X        D        d          D     X        D                    D                                  <                  D          E                                  <                  D      [  E                E  
       E"     	      E                                  <                  E     @E                                  (                   E                     $  0  <  H  T  `  l  x            -                 	E          (        
E             E  4     4    %  8       <     H0                  <                                                                                  ,                            E                    E                      E                      E                     E        D           E                     E        X             E                      E                     E                    E                     E                    E                      E                    E        4          E        d            E                    E                     E                    E                  E                    B                    %                              B  
                   $       B              B           %   B  ,                                                                                                                            | ` d l     <                B                       L          p               x t     B                     $       $      B              C                  B           X                 <        \                         B                               B            l    h                                                 H  
      ,                 H     T #    $     H        H        B                       B                       L                
         F                       L                                 B              B        B                    B                       L               
 
         B                      B        B  
                      E
C        B  
                          B        %         ʸ#E        "     $E        7R| (   %E        촁";&E  
      8Ҕz>R   'E  
          Y'Ђ<r (E  
      8Ҕz>R   )E           m&!pm (m     *E               Z7ӟS(   +E                w=!/o   ,E                 Za)B;	 -E  
          Y'Ђ<r .E               Z7ӟS(   /E                 Za)B;	 0E                          <     <                 2E        3E                          @     ( @  1E        t      l  5E                  \  6E                     7E                    8E        X            9E        t            :E                    ;E                  H  <E                    =E        4            >E        h          4  ?E                 @E     X        AE                     BE                      CE        D             DE                 EE     X        FE        P            GE                  8  HE                   `  IE        h            JE                    KE          0    L  LE     X   (     ME        X             NE                     OE                  B        pE  
                d @;  E  B                                    , ,   D H             P                                 ,@                                         L                                                                                         E               E  
      ,              5  E        E  
      ,              i  E                                     <              C            H  L  X    < P  E         q6     E           @T  @OE               E                4d   E                   E                4d   E        "zo9   O4E             E             >      E           R
   E        Nm]   E  
         	iï? )}	     !E  
         	iï? )}	  "E  
             
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              	                                                                                                                                                                                                                                                                                                                                                                                                                                                                        P
                                                             
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     L @                              H                  0        @         P     a  !  `         p                        C         D            H           L            P    D     T    H     X           \           ` X   L     d X   P     h X   T     l X   X     p X   `     t X   h     x X   p     | X   t      X   x      X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X          X         X         X         X         X          X         X         X          X   (      X   ,      X   0      X   4      X   8       X   @     $ X   D     ( X   H     ,    L     0 X   P     4 X   X     8 X   \     < X   `     @ X   d     D X   h     H X   l     L X   p     P X   t     T X   x     X X   |     \ X        ` X        d X        h X        l X        p X        t X        x X        | X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X         X          X         X         X         X         X         X          X   $      X   (      X   ,      X   0      X   4      X   8      X   <      X   @      X   D      X   H       X   L      X   P      X   X      X   \      X   d      X   l      X   p      X   t      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 X        $ X        ( X        , X        0 X        4 X        8 X        < X        @ X        D X        H X        L X        P         T X   $     X    <     \    0   < `    @   < d         h X        l X        p X        t X        x X        | X         X         X         X         X         X         X         X         X         X         X         X         X         X          X   $      X   (      X   ,      X   4      X   8               X   <      X         X         X         X         X         X         X          X         X         X         X         X         	 X         	 X   $     	 X   (     	 X   ,     	 X   0     	 X   4     	 X   8     	 X   <      	 X   @     $	 X   D     (	 X   H     ,	 X   L     0	 X   P     4	 X   T     8	 X   X     <	 X   \     @	 X   `                         B                      B         $       B                     B       M                               J                   B                B                     %          @ʸC          4        1                               L                                                  M                        -      N    3                                                    4          O              6                                          	         7         
                 5        !                      %                                  )          !  8      +          #  9                "      /          '  :        6      )  ;      !  7          P  5                  %  8        #                      ;          3  <  	  =                                                    C                                  G          ?  =      I          A  >  Q  9  :              )               O          5  $  R  ?  <      7  %      S                          ;  &      3   
              Y          Q  ?              S  @              C  '                      a          Y  A      Q  =      I  (      e          ]  B      g      6  M  )                  S  k                  m                          U  *  T  q          i  D                      Q                                         q  E      i  >                                                        g  +  U                    s  ?              c             V                      !   <  q  ,  W  {  A                                      w  -                         "                #       }  .        C        /      w                    $                         0      }                  %         G        E                 &         H                1                  X     '         I        F                                 (                )   B    2        H        3                                                         *                 +         4        J          Y     ,         K         -   D    5                                M        K        6                                   "     .   G    7                                                         M        8                          /                         9         0         O         1         P                   Z     2         Q                :                         3                  4   I    ;                <                                S        N        =         5                         T                >        6         U        O                P        ?  [    7                                                  8       	  V  *    9     	  W                                          :                 R        A        ;                 <                 S                                                                 %  =       	  X        T                                      #	  Y              %	  Z                B      !  !              3  >       +	  [                C  \  7  ?       /	  \  0  9  @                               =  A       5	  ]      -  V                                                                                          2  K  B   
  C	  ^              3  E                      Q  C       I	  _                              M	  `      E  X      O	  a  ]  G  Y              [  D               ]  E       U	  b              E  F      a  F       Y	  c              I  G      A!  $              g  G       _	  d                      Y  Z      Q  H      I!  %              o  H               _  [              O!  &      k	  e  7  u  I       [  I                              q	  f  9  {  J               Y!  '          ^    K       w	  g      o  ^              _!  )                L                                                                 M       	  h                        N       	  i        _      y  J        `              s!  *      	  j        O                         K                        a              }!  +                P       	  k        Q                               !  ,                      	  l        b        L        R                 S     	  m        c        N              	  n  ?    T           _    e          `    U                 f        O                        V                         P      !  /        Q                        W                         R        X                 Y   !  	  o                  a    Z                 g          b    h              !  2                                                [                   #  	  p        i              !  3                \                 j        U  c    ]       	  q                                                        ^       	  r                V        _       	  s        k              !  5                `       	  t              	  u  d    l                                      	  v        m        W  e  	  a                 b           f    n                                                              !  9                        X      !  :                      
  w        c         Y  g    o        Z                      #  d                               "  <      
  x              !
  y                [  h  -  e                 p                q        \  i  3  f               #  r                              9  g       1
  z    )  s      !  ]      +  t      #  ^      "  ?              A  i       9
  {      1  u              !"  @      =
  |              -  _  j  7  v      /  `      K  j                               +"  B      5  a      Q  k       I
  }      A  w              1"  C              W  l             G  x      ?  b                      9"  D              _  n       W
  ~                                    S  y                      M  c      i  p       a
        k  q   4  c
                        K"  E      g
        _  z              O"  F                              w  r       o
                                                u
                          s             q  {  8  {
        s  |      k  f  k    u       
                
    l  y  }                v       
        }  ~                                w       
          x       {  g      s"  I      }  h      u"  J                      
                                
          =  
        "  K        j        z                       
    m              n    {                         k                              
          |       
        "  N                                                                }       
                    o            l      "  P                @  
    p            n              
                  o                                                                 p                               
                        "  R                                               "  S      
                q                                                 r                              
             H  
                  t                               
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	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	           	          !	          "	          #	          $	          %	          &	          '	          (	          )	          *	          +	          ,	          -	          .	          /	          0	          1	          2	          3	          4	          5	          6	          7	          8	          9	          :	          ;	          <	          =	          >	          ?	          @	          A	          B	          C	          D	          E	          F	          G	          H	          I	          J	          K	          L	          M	          N	          O	          P	          Q	          R	          S	          T	          U	          V	          W	          X	          Y	          Z	          [	          \	          ]	          ^	          _	          `	          a	          b	          c	          d	          e	          f	          g	          h	          i	          j	          k	          l	          m	          n	          o	          p	          q	          r	          s	          t	          u	          v	          w	          x	          y	          z	          {	          |	          }	          ~	          	          	          	          	          	          	          	          	          	          	          	          	          	          	          	                           I    ,˸	      k   !                    <            %   P   a       1     d          o   ?   x            i      #       u  -      v      7         I          ;             g                Y        }                    '                   ,  s       A      @  y      x  z  T  =       c     h         e   ~  |         y               |    ]                          +      U                          O                   _       M     0          {   D            X           
   l  P                 
       l      x  x                  9                       $    {                      <      H      ~  \                 4  V            H  
           \               p                       8                  4                                 D                
 
     ,!       @                $         D!    8           P! L        ?       `          	   t                            "        !      $         !                               !                           &       \!    (  
         h! <        ,       P           Q   d  !       T x                   I       !               "                                 !                              _       !      p         ! ,          {       @         T    T  X"       , h               |  q       p"      X         "         5                8 k     4"                                    "               "         S       0         T X   D  "       t X               l         "      
         "           U                H      #                              N     8 8       $u I  0	      `       
         l       x        x        9               :       $       
        <       <        H       \ .       T       < V              
                                             8 +               4               '              d D              
 
       ,!      @        8!              D!              P!      ( ?               	               7       !       "        !      $        !              !              !               !       &       \!      
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         u       $ T       @        "                #                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     	          
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S                 R                                  LK                                                                     S                     R              R                  L                  R                     '\                     R  
               PK @K     ^L                  %S                     L                  R                     L                 R                      t1                                                                                 R                 R                  R              K L                  S                 R                     R                  "S                      X3 3 L L L L p Lp p p L 2 x2 dL `L XL TL LL     @L 8L    R                     R  
                K     L                  R              8                $1                                                             q J     R                  6L              n                 <1                                                                     tK R                 R                     R                  R                  mL                 S                  +S                     R                  R                  S                      0p p K L  L 2     ,L L Xp lL \L <L K 1 K K         K 1     hL  
                E  PD  `D  R                     R                     R                     R                      o         q K                         K K (2 K                             ]L                    R                 R                     R              K     p         hq `q                 xL n K K L p K K                     cL                      0q         o K                         PL L K 1 K K                     R                 R  
                  pR                     NL                     R                      lo L K K K 0L     hL L P2  L K K 2 K K K                     R                  R                          pK                                                         Lq ,2                 R                              8K                                                                         PK R              $1             hK     DK xK                                                                 R                 R                 ;L                 R                          n             dK \K                     XK 81         HK x1                 OL                 DL                                  ,K                                                             K         R                 n R              n                                                             J                         K L                 J R                     R                                  `K                 TK K                                     K K     R                                                  0                                                         R                     W        X        R                     &L                  R                                                      J                                                     R                  R                     R                                                          J                                                 +L                                                              J                                             R                                                      J                     J J                         R                     R                   K                                                                                          xJ                R                     R                                                                                                  lJ         [                          p             q                                         $q ,q             [  "      0                      <              8n           @W   "         q
 |n                                     [                    [                 [                                        &           ,T           h                   y              K             G   t           ( P $                 &     & u                   $                            [                                             p                         (q                                [                                     p                                     p                         [                 	                                                                       [        t                  $               Ln         u                   $                           [                 [                                                                                                           [                 [                 [                     9k                                N	 H    4   ,    P   T   L       (  ˸              n                   *                            *&                 T                 6              $ PL K \L K LL lL @L 4L K L K K 0K L K TL K L K     8L $L    v              \   v                 V   v              ,  v              |      )                 v              v              ,b                    v              >      v              j   v                                                       v                 xv              v                                     v              x2                    v                 v                                  v                    v              N   v              y                 Ly              L   V   y              Py              8              $ t    ̉  `  x L   T   8  Ti      ĉ \    u              X   v              w              b   ^   x              X  #                     '                 {              8f                                          ~                              H                 X%                                     *                               44                                                                                                         
                 h                                          |,	              (   N              ~N                \  V              P   Fi  
               5   z                 Nz              2  `                 z              j   z                    B                                     z                 z              (   ]                    O                 z                 Nz              T              	   z              7                     &                 z              `  z                  {                  ~{              &    D              |  5x              P   6x                 n7x                               9x                 *8                    ;x              *   j@x                                 J   Bx                 R                 Dx                 nEx                Hx              B   Ix              T   Mx                               Ox                 Px              h   Vx              Wx              >   :   Xx                 Yx              Zx                 [x                            <= H= = l= = = 8= t= = = = X= h= LU `= T= \= = $=     = x=     Dv                   
            n;o    w                    T    8 x     <                                     n Pn ,n n n \ Xn n n `n n n \n Tn <n pn 4n @n n     dn tn     @  %T                          8	   
{                 c                 {              j  
            $   ;o    %                    {              4H   {              \   \{              >   4  8                     C                 Li{              &  \{              {              b{                {                    {              r   {                 V{              V"   _                    {                 x   {              v                0  ˂                 p̂              r͂                 ΂              .                "   Ђ              т                 n                                  ڂ              v   .                    ւ                 .  ׂ                 ؂              ق                                        ۂ              nm                 0n              <z              z                    z              N   z                 N                     A                  	   z                  h  0                     1                    z              .  6              .       4                 l#z                 6z              p   P   `u                    nu              "   ou                 &                     "                    yu                   u              |  B     E G `G Q |F > a @ c e `h Hl Tn Q Pt dX LZ O Z . %   |4 d.        ܆ P           \       x  @ x	 % '  5 @  G O C R Z  m t i  ̌  p  ,U 8   P  8 ` .       X  H   #  2  T h2 U A R 7 8p " } X {   (z  HO ʸ              `H	   (             8d	                  6                               (   @              v  B                  i                                                   y              2   y              T:                                           y              $  y              &   \y                 ly                 y              (  y              H   z                  6 6 (7 P7 X7 \7 T7 7 H7 7 6 6 $7 @7 6 47 6 7 D7     07 6 <  y                 y              (  t                 y              X   y                    y                 :~              b^              4+ P+ + 0+ @+ <+ + + l+ p+ (+ T+ \+ + + `+ + + +     x+ + 0  
            b;o                    3 3 3 t3 (3 3 @3 $3  3 3 83 3 P3 l3 3 H3 L3 3 D3     `3 3     @  ~                             J  `K              cu              N  Lmu                 B|              	   	   ku                 +                                     *   u              F  u              Hu              \                 n     ^_                     7]                dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr                                                                                         dr 4x i_                                  <        ` d        l_                          $     $       } }         V`                     W`                     n_                 o_                     r_                  p_                 q_                     t_  
                }     s_                     x_                    .]         u_                     v_                 w_                     |_                     }_  
                   }     y_                 z_                     {_                    _                     _              _                     ~_                 _                 _                    _                     _                    _                 _                 _                     _                  _                     _                     _                    _                     _                     _                    _                     _                 _  
               H~     _                    _                 _                     _              _                     _                    _                     _                     _                  _                     _              _                     _                    _                     _                     _                     _                     _                     _                  _                     _                 _                     _                 _                 _                  _                     _                     _                 _  
                  ~     _                 _              _                     _                     _                     _                  _                 } _                 _                 _                 _              D~ _                 _                 ~ _                 _                  _                 _                  _  
               (     _                 _                 _                    _                     _              _                     _                    _                     _                     _                  _                 _                     _                 _                     _                 _                     _                  _                 ~ _                 _                 D~ _                     _                 ~ _                 _                 ~ _                 _                  _                  _                 D _                  _                  _  
                        _                     _                 _                     _                     _                 _                  _                     _                    _                     _              _                     _                 _                     _                  _                     _                     _                     _                 _                     _                     k_            `                 } `                 ~ `                 4~ `                 T~ `                 t~ `                 ~ `                 ~  `                 ~ !`                 ~ "`                  #`                 4 $`                 T %`                 t &`                  '`                  (`                  )`                 *`                 +`                     ,`  
               X     _                     _                      `                     `                     `                     `                     `                     `                     `                     `                     `                     	`                     
`                     `                     `                     `                     `                     `                     `                     `                     `                     `                     `                     `                     `                     `                     j_     p     0 x~ , ~ ( ~ $         ~    h  h  h~  ~   ~  ~  X  $~  (    <~    ܀ L~ ؀ } Ԁ  Ѐ l ̀ } Ȁ ~ Ā |~  ~  8  ~  ~  ~  X~  }  }      ~     ~ ~ ~ ~ ~ ~ ~ ,~ ~ D~ ~ } ~ ~ ~ }  ~  0    , $ H 4 8 @ } D ` < } P L T x d X \  p  l } t  |                                    $ ( , 0 4 8 < @ D H L P T X \ ` d h l p t x |         ~ ~ ~ t~ l~ \~ p~ `~ d~ T~ H~ P~ @~ 0~ 8~ 4~ (~ ~  ~ ~ ~  ~ ~ } } } } } } } } } x} \   4    < @     -`                     .`                 /`                     0`                     1`                  2`                  3`                 4`                 5`                     6`                  7`                 8`                  9`                  :`                  ;`                 <`                 =`                     >`                 ?`                     @`                  A`                     B`                  C`                  D`                 E`                     F`                     G`                     H`                  I`                 J`                     K`                  L`                  M`                 N`                 O`                     P`                     Y`            Z`                 [`                 \`              l  X`                                                        
      	                                  !      "      #      $   %   &   	   '      (      )      *      +      ,      -      .      /      0      1   
   2      3      4      5      6      7      8      7      6      5      4      3      2   
   1      0      /      .      -      ,      +      *      )      (      '   	   &   %   $      #      "      !                                  	      
                                                                                                 !   "   #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   4   5   6   7   8   7   6   5   4   3   2   1   0   /   .   -   ,   +   *   )   (   '   &   %   $   #   "   !                                              9   :   9   :       &S                     S                  [                 [                  9\                 	S                  ,S                     
\                     [                 [                     S                     R  
               K   \                 [  
                           [                     [                     [                  \                  [                 [  
                       [                 [                  \                     \                     \                 R                     R                 E  rL                 [                  \                 [                     [                  ,\                  [                 \                 \                    \  
                       \                     	\  
                ,p      \                 R                  R                     R                     R  
               `YP\                 8S                  6S                     [                     [                     [              q     (n     o n o $o     `o o 4o Ho ,o Po |o Xo To xo                    \              D      <p |p p dp Dp Hp o o @o p Pp p p p p q L L     L L d>  \                  #\                 \                     R              [    4q         po 1                                 tL K                             \                 !S                     #S              [              	      n Lo Do (o o <o     n ho o o o o p o o o         o o N  \                     [                     \                 [                 \              -\                  \                 2\                 !\                  "\                  \                 R              n     q                                                                                     -S                     .S                 \              _(\                     %\                 \                 4S                  n                                                                                         [                  [                 \                     [                    \                 [              @      o o o o o o     o n o \o o p  p p p 8p         p $p ,y  L                     S                  R                     S                     (S  
               Xp p [                  S                 S  
                   2     L                 R                  S                  R                  |L                     R                  R  
                  E  E  R                     S                     L                  S                     5\                 2S                    7S                     &\                     D\                 \                     $\                 L                     S                     S                  XL                  R                     \                 R                  {L                     *S                 L                  5S                     [                 )S                     'S                  0\                 S                     1S                 L                     L                 $S                     3S                  L                  R                     R                     [              .\                     0S                 L                 R                     R                 R                    S                 S                     S                   S                 S                  S                     /S                 R                 S                  R                     S              L                     S                 S  
                   @  M]        J]        S]                                  <        u (u         B]        %      <^        [                                                  p                     p                         Pm[  
               n     d\                 `-[         ,n          $             A]             d   q                                                                                         Pr                                                                                         q                                                                                         r                                                                                         q                                                                                         xr                                                                                         q                                                                                         8r                                                                                          r                                                                                         q                                                                                         Dr                                                                                         pr                                                                                         r                                                                                         r                                                                                         q                                                                                         @r                                                                                         hr                                                                                         q                                                                                         \r                                                                                         q                                                                                         q                                                                                         Hr  ,]                       u   ,n     ,n :   :     t         \                 `-h\                 [                 [  
                       _\                  9N        1N        #]            H f     0   t     g        }     h        }     i     0   @n     j        t         \                 N                       u   =     =       lu :         N             \                    \                 L \                    3N        N        \                 ˸\                    \                 N     8 8 <8         \                    \                     \                 \                    \                    8N            .C   \                 ~\                    .N                    \                     {\                     y\                  N          w\  
                         [                       x>           N  
   ,6 4l    x>          M                                  4l       p6 6         KN     X9 H9       ʸ\                     \                     \                     v\                 ,N            d7         V\  
                       t Y\                  Z\                 b\                     U\  
               q         R\                 G\                 T\                 O\  
                           S\                     M\                 Q\                 c\                 I\  
                           N\                 H\                  L\                 K\                  J\                    7\  
                       C\                 W\                 >\  
                       F\                 E\                 HP\                     =\  
                           B\                 A\                    @\                     ?\                  ;\                     :\  
                          \              D       o  p p o do  o hp o o 4p \p p Tp pp tp p lp p     p p N [  
            n  o     [                 [                 [                 [                 [                 [                     q         Xq dq                             q Tq Hq                             [              [                 [                    [                  Dq         pq lq                         tq xq q q r                     ˸[              D]    |q         n n                     n n n n n n n                 [                     [                  [                     \                 [                     [                  [                 [                 [                 [  
                  ;o,  [  j       :      2               X    "         3  x\          &      ܿ    (          )                +          ,                .   	                 0          1          2          3          4          5          6          7          8                   /   
       9          !   \                 [                     [  
                o     [                     [                 [                 <\                 [                  [                 n [                     4\                     6\                     [                 |\                 s\                 r\                 q\                 k\                 M                          $     $       @: `:                 N                                                                 ʸi\                 ,  X\                 `\                 \\                     [\  
                        ^\                 ]\                  ]`  "      0                      <              D A   :       @WC   P   :   K   i x                                     c  D      #   C   /   3   5   9   ;   ?   A                   
                                                D             !   "   E   $   %   &   '   (   )   *   +   ,   -   .   F   0   1   2   G   4   H   I   J   |         l          ~   ^`            
                                                                                                                                                                                                                                             I         J                   D   `                         !          "          #          $   E   f             &          '          (          )          *   C      +          ,          -          .          /          0   F   r             2          3          4   G   v             6   H   x                                  |                  ~                                                       	               l                       %          1          5          7          8          9   L           M           N           O                           [           D148 0  
   $                      M  "           (; P                                                                                              ?Q  
   Print(D148); sition(M148);  [  
      /              t       N                P     D8 7        M     ;         uN      9    9     f]              J    F]        8]                       9           c      (; Q d M                     X:    9     ~N     @6         C]                                            %       t   (:               ˸P               Ъt     D x( 4> G hM |( '     G ?  m     C G C = = |= h= t' ʸ        P     L6 #N        XN                     X:    8     HN     `9         WN                                  9       P9 x9         RN                                  <        8 D9         @N        tN                                  <        9 9         ON                                  <        9 9         qN         T  M       <]           J           M  "         D 3                        $     c        X:     d     0   Hu     e        r                   R]  "      0                      `u             z    r       U      r      [e z      ww ww       5`5    ]P     8 7    M        M        j]        ]                       L   Pu     Pu       u u         ]        !   J   s]        ]           J   v]        ]                       L   Pu     Pu       v u         ]           J   ]                       L   Pu     Pu       v ,v         ]        3   J   ]        ]        =   J   ~]                o]               }]        z]           J           u]        A   J   i]           J   %       G]                                                                   e]  
            S           T]        M                            J   %   ,u           8u     W]      Pu    J      Q]  
               $   MʸX]                       Pu           7^               q]                p]        K]                     %                    O]              U]           %   Q_                       L   Pu     Pu       u u         D]  
   
 `u    Pu           N]                    %                              h]  ,                                                                                                                            Du xu tu Xu     u                `]                       L         Pu u                <u Tu     _]                  $   ]]                     ^]           v                 <        |u                         V]                     ]_        ]            Xu    lu                                                 `N                                  (        9 9         zN                       <            ?N        ]           J   5]        m]        ]        5   J   |]        ]         N     A 7    M        aP     %       d]                          $     $       u u         g]     q        b]  .         $          J       o                  p        u     m        u     q        Lu     r                        $     s        u u S_                       L   Pu     Pu       u u         )]                       L   Pu     Pu       t t}         6]                       L   Pu     Pu       |t t         Y]           J   @]                       L   Pu     Pu       du 4u         $]           J   R_        ?]                       L   Pu     Pu       t H}         n]           J   k]        H]                       L   Pu     Pu       u u         c]        5   J   x]        ]                       L   Pu     Pu       u u         ]        -   J   ]        ]                       L   Pu     Pu       v v                 ]        !   J           w]                       L   Pu     Pu       u u         ]        ]        9   J   ]        l]                       L   Pu     Pu        v u         r]                       L   Pu     Pu       hv u         t]                       >]        %   J   ^        ]        ]                       L   Pu     Pu       v 8v         ]        '   J   ]        ]                       L   Pu     Pu       0v Xv                 ]                       L   Pu     Pu       u v         y]                       L   Pu     Pu       u pv         ]           J   ]        ]                       L   Pu     Pu       4v Tv         ]           J   ]        ]                       L   Pu     Pu       xv lv         ]        G   J   ]        ]                       L   Pu     Pu       v |v         ]           J   ]        ]        9   J   ]                ]                       L   Pu     Pu        v v         ]                       L   Pu     Pu       dv u         ]           J   ]        ]                       L   Pu     Pu       w Pw         ]        E   J   ]        ]        3   J         ]           J   ]        ]           J   ]        ]        ]        ?   J   ]        ]                       L   Pu     Pu       Lv v         ]        C   J   ]        ]                       L   Pu     Pu       `v v         ^     %      J   ^        _                       L   Pu     Pu       t z         |N             g^           J   R^        ]^        _^        =^           J   D^           J   >^                ]                       L   Pu     Pu       v Dw         ]                       L   Pu     Pu       v v         ]        +   J   ]                       L   Pu     Pu       v 8w         ]           J   ]        ]        	   J   ]        ]        =   J   ]                       L   Pu     Pu       v v         ]                       L   Pu     Pu        w v         ]           J   ]        ]                       L   Pu     Pu       v v         ^        	   J   @^        ^                       L   Pu     Pu       |x  y         ^           J   ^        $^                       L   Pu     Pu       hx lx         %^        1   J   -^        &^        ]                       L   Pu     Pu       `w hw         ]        ]                       L   Pu     Pu       w xw         ]           J   ]        ]                       L   Pu     Pu       w w         	^        ?   J   ]        ]                       L   Pu     Pu       $x w         ]           J   ]        ]                       L   Pu     Pu       w w         ]        G   J   ]        ]                       L   Pu     Pu       w w         ]           J   ^        ]        -   J   ]                ]                       L   Pu     Pu       v v         ]                       L   Pu     Pu       w v         ]        ]                       L   Pu     Pu       w v         ]        7   J   ]        ]                       L   Pu     Pu       v v         ]        #   J   ]        ]                       L   Pu     Pu       w @w         ]     %      J   ]        ]                       L   Pu     Pu       4w w         ]        '   J   ]        ]                       L   Pu     Pu       Lw ,w         ]           J   ]        ]                       L   Pu     Pu       w $w         ]           J   ]        ]                       L   Pu     Pu       0w Tw         ]        A   J   ]        ]                       L   Pu     Pu       Hw |w         ]        C   J   ]        ]                       L   Pu     Pu       \w w         "^        )   J   '^        ^                       L   Pu     Pu       x x         aN                                  <        49 8         ]N                                  (        d9 T9         iN                     X:    8     +N     9         )N                                  <        ` 8         -N                                  (        l8 8         M        	N               8     0^                       L   Pu     Pu       x x         ,^        ;   J   H^                       L   Pu     Pu       x x         8^        7   J   )^        ^                       L   Pu     Pu       x x         Q^        1   J   (^        *^                       L   Pu     Pu       Dy x         +^        I   J   5^        /^                       L   Pu     Pu       x x         3^        I   J   ?^        .^                       L   Pu     Pu       x x         2^            J   Y^        6^                       L   Pu     Pu       x dy         t^        $   J   i^        ^        %   J   ^        T^                       L   Pu     Pu       y Hy         ^        &   J   u^        q^                       L   Pu     Pu       `z y         n^        (   J   |^        v^                       L   Pu     Pu       y y         y^        *   J   ^                ^           J   G^                       L   Pu     Pu       x x         `^                       L   Pu     Pu       y x         ]                       L   Pu     Pu       w @x         ]                       L   Pu     Pu       w w         ]        /   J   ]        ]                       L   Pu     Pu       w w         ]           J   ]        ^                       L   Pu     Pu       w w         ^           J   ^        ]                       L   Pu     Pu        x Px         !^        #   J   ]        ]                       L   Pu     Pu       x w         ]        )   J    ^        ]                       L   Pu     Pu       w  x         ^           J   
^        ^                       L   Pu     Pu       x (x         ^           J   #^        ^                       L   Pu     Pu       x x         ^        E   J   ^        ^                       L   Pu     Pu       x x         ^           J   ^        ^                       L   Pu     Pu       4x Hx         ^           J   ^        1^                       L   Pu     Pu       <x 8x          ^        +   J   ^        ^                       L   Pu     Pu       x x         9^        /   J   ^        ^                       L   Pu     Pu       x Tx         ^        ;   J   ^        ^                       L   Pu     Pu       Lx px         ;]     ˸L   E   N   D}                  <                  P   x         (w d                  x          L}               G   tv        	                 Dv       v         Xw    H                    u       w     L   v               ,          v    @  x         T          '   h          w %   |   u     K   u                   }  v                                Dx ?             I   u             7               0  v         D  D          X          u    l              w                                  w               8             w -             J   $v                 #                  x         4                 H         (v    \   u         \v p                          w      v         v                    !       <w (     }          D}       *           u              $  9          8  t     H   L            `      tv    t             @v                         t                           v                 dw              =           (  w         <          (   P      u 
   d              x                        v                   ?         u 	                w             "             <v         ,            @      w $   T              v h         |  &             w                  -         $v                 v                                     0          D              (w X          l               0x                   1         Dv                  Xw             w wN  $                  3                   J            u                      $          z          H:     []  "   x= p= \= =  = L= @= 4= < < < B m 0C 8C ,N M  ' <' PC LN hC `C tC xC H4 C C TC C    VN                                  <        L9  9         (N                                  (        ,9 09         DN                                  <        8 8         "N                                  <        9 8         0N                                  (        9 9         N     ` 8     M        N     9         K^           J   :^        ;^                       L   Pu     Pu       ,y x         h^           J   E^        B^                       L   Pu     Pu       y y         C^        
   J   M^        A^                       L   Pu     Pu       y 4y         F^           J   X^        S^                       L   Pu     Pu       y `y         O^           J   p^        N^                       L   Pu     Pu       <y y         I^           J   L^        P^                       L   Pu     Pu       $y 0y         V^           J   j^        Z^                       L   Pu     Pu       Xy y         \^           J   W^        s^                       L   Pu     Pu       py \y         ^        6   J   ^        ^                       L   Pu     Pu       z 8z                 ^                       L   Pu     Pu       y y         k^                       L   Pu     Pu       y z         P]        w^                       L   Pu     Pu        z ty         [^           J   ^^                       L   Pu     Pu       ly |y         b^           J   o^        U^                       L   Pu     Pu       y y         f^           J   ^        e^                       L   Pu     Pu       y  z         z^            J   c^        l^                       L   Pu     Pu       y y         m^        "   J   d^        a^                       L   Pu     Pu       y y         ^        D   J   ^        ^                       L   Pu     Pu       z z         ^        F   J   ^        ^                       L   Pu     Pu       { z         ^        H   J   ^        ^                       L   Pu     Pu       z z         ^  
      ,              Pu ^                       ^                       L   Pu     Pu       z z         lN                                  9       9 =         uP                N        M        ^        8   J   ^        ^        :   J   ^        ^        r^                       L   Pu     Pu       y z         ~^        ,   J   ^        x^                       L   Pu     Pu       y lz         ^        .   J   {^        ^                       L   Pu     Pu       z y         ^        0   J   ^        ^                       L   Pu     Pu       z (z         ^        2   J   ^        ^                       L   Pu     Pu       4z z         ^        4   J   }^        ^                       L   Pu     Pu       \z y         {]  4   (   t d   p0   x d      $    u                  $                    6	                            $                            u                            Z]  
      ,              I   AN                    ^                       L   Pu     Pu       z Pz         ^                       L   Pu     Pu       Hz |z         ^        <   J   ^                       L   Pu     Pu       Dz z         ^        >   J   ^        ^                       L   Pu     Pu       hz Lz         ^        @   J   ^        ^                       L   Pu     Pu       tz dz         ^        B   J   ^        ^                       L   Pu     Pu       z xz         ^        	                  =   Q   )            1   %      #   5      /      K         W                              -   ?   3   V   7         I   S      U   ;            O                  +   9         M            '      !                     Y   A      
                                              (   *   ,      .       "   $   &   8   :   <   >   0   2   4   6   H   J   L   N   @             Dv            y    1   u 	   y         u        t        Pv        (v         w        \v        v        v    J^  B                                    u ,  hu @u             # $u                         ,x                                         z                                                                                         I]  4   (   t d   0   z d      $    `0{                  $                    6	                            $                            $u                            ^            D 3                        $     c        (y     d     0   Hu     e        r           \]        ^        y N      D}         y O       u        Ly P      x 9       8y Q      t        x J      L}        y K      tv        y L      @v        x M      v        y V      t        xy W      u        Ty X      v        y Y      dw         @y R      x =       hy S      w '       y T      <w (       Py U      u 
       y _      dx A       y `      v        y a      v        z b      Dx ?       y Z      u 	       y [      w 7       0z \      v "       y ^      <v        <z g      u        $z h      w $       Tz i      v        pz j      w &       @z c      w 8       z d      w -       z e      $v        ,z f      v #       z o       x I   F   L}     G   tv         @v     Dv     z k       (w )        { l       Hv        Xz m       0x ;       z n       tw 1       dw     Dv            Xw *       w     w ,       w %       w    K   u     x H           M   v         v             I   u                 v     D   <v     E   u         w         v         w                     J   $v         v                 v     Pv     (v      u     \v     t     v     w     v     v     v     v     <w     Мl                            9                                                                                                      =          '           (          
                                       ?          	          %           "                               $                     &           8          -                    #                                       v !      w 0       v        \x <       x :        u        \v        lw .       `x 5       t        w 2       v        pw +       w 6       v        v        w 3       v        Pv        (v        w /       ,x >       w        w 4       Xx @       tx B       x C       x D        y E       xx F       x G       y ]       z p        q                                                            4^    8˸                  lr           q     @              P          `          p                                 v       v                           t       v                           v       Pv                          pw 0     lw .   @     /       P         w `     w 3   p     4                w      w 7        :                ,x           y N                         u       Ly P        9                t 0     x J   @            P        tv `     y L   p                    v      y V                       u      Ty X                       dw      @y R         =               w       y T   0     (       @        u P     y _   `     A       p        v      y a                       Dx      y Z        	               w      0z \        "                <v      <z g                0        w @     Tz i   P            `        w p     @z c        8               w      z e                       v      z o        I                                             0     z k   @     )       P         Hv `     Xz m   p     ;                tw                               Xw                   ,                 w                    H                          0                    2]    8˸                         <               P           d                   x                                                                                                                                     ,              @          T                  h              |                                                                                                                              0          D                  X              l                                                                                                                                         4                  H              \          p                                                                                                                              $                  8              L          `                  t                                                                                                                               (              <          P                  d              v x         0                \x <     x          u                    .       `x 5     t         w                    +       w 6     v         v ,          3       @         Pv    T  (v         w h          >       |         w 4     Xx         tx           C         D        y E     xx         x           ]                                                         0                  D                 X              ثl                                                                                                                  ^    8˸                      r           r     @              P              `              p                                                                                                                                                                       0             @             P             `             p                                                                                                                                                 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;     N                N                                  x>       @; P;         N     t6         O               M        I     :     M                                  <        : P6         O                                  <        : 0l         [        N     t> 6 $˸Z        Z                                  (        : k         M                     8     d     O     7 @       N                                  x>       7 D;         M        P                O        M     <               P                                  <        H> 6         N                                  <        & ,>         O        bN     L; B $˸M        M                                  (        9 h6         M                     8      ;     WQ                N                                  x>       6 t7         M     7         O               N        N     >     O                                  <        B l>         Z                                  <        7 Pk         Z        M     j T>  ˸N        N                                  (        7 :         N                     8     >     NQ                UQ                                  x>       > \E         N        P                O        O     @               N                                  <        |> :         M                                  <        : n         [        Z     6 4;  ˸{O        'Y                                  (        k =         N                 'Q  
                       $Q        I                  M                                  x>       : :         N            XI                                  <        lB >         N                                  <        ? =         }O        O     ; $ ˸P        N                                  (         ? tB         M                     8     >     qO     6 H       QQ                                  x>       s 8E         O        J                MQ        SQ     D               M                                  <        d: :         M                                  <        H; 4s         N     B       \        RQ     `7 (6 ʸOQ        }J                                  (        HE <E         M                     8 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     xM                                  <        p7 6         N                                  <        6 6         M        Z     ; 5 ˸O        M                                  (        tj @>         N                     8     =     \     0; D       N        M     l6 N        M                     8 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    h>     M               P        N     *             O                                                                                                         O        )                             8  9 M                                  x>       6 `6                 Q                 Q     G 4M    P                  |O                  Q         C        $                       O        O              P                  P                 ;K              ,     P              O                 P                 P                  O                 [                 O                 P                  P                 I                 O                 P               P                  |[                    I              P              N                  N                  N              hO                  aO                  _O              06 ZO                     I                  zS                  Q                 N                    O                                  <        Lt ?         ]               KQ                                  <        > 0E         \                                  <        E $E         AQ     ds ,E ' HQ        nJ                                  (        E  E         <Q        ?Q                                  x>       D s         &Q     :         +Q              *Q        \        %     BQ                                  <        s <s         tJ                                  <        D D         6Q        @Q     ) E ,D \        \                                  (         E s         \                 P  
               I \                     8     D     7Q                                  x>       D D         2Q     r         4Q        :Q                                  <        D D         _J                                  <        s )         eJ        9Q     |) D $˸8Q        ;Q                                  (        D D         9]                 5Q             GJ                                  <        D D         3Q                                  <        s t         \     	   %      N     D )     /Q        .Q                                  (        ; D         a]              6K                     O                   Q                     O                 (]                  O         t                  $       G `? ?         u                   $                                   Q                  \                  ? '                 F     ?             ?         ?         ?     $@             ?         p?         ?         ?         G     (@             |?     X?             ?         D?         G         dD         D     ?             (         6         `     >             D         D         D     B             =         tD         D     :             >         B          H     TD             ;             >                 D     t         C         <D     hQ                 Q                 tQ                 ^Q                     nQ                 iQ                  O        )                         ? (  $         V_                 [                 J                     M_                    pQ                 b_                 P                 G     s B 4> 0? , @- G     Tr     C     : D D = = |= h= t'     EO                 ڋ                 oJ                     \                 _Q                 lQ                     Q                  ]                 `Q                  J                 O              zQ                 uQ                 jQ                  mQ                 P                                  <        d8 =         ZS                 N                 <M O                 P         h?    ,n G                O              (                                                                                        $@ O              C O                 ( O              dN                 P                     Q              O                 C \                 	P                     O                     Q              O              $ Q                     O                    R[                    I                 P                 O                 O                 ˸
P                  O                                 	   
                              O                 Q                    O                 O                 ,Q                 O                 Q                  3J                    O                     M  4               C         B 4> & B     B     ; > B     |; B = = = |= h= t'         C m     & B hB t;     B > $>     B dl >                     `l 8X                 | >Q                  M                     %Q                 x1K                  O                 (Q                     O     r t?          $ G `?         	)Q                     wO                    Q                 P                 Q                     "Q                 || O                     N                  R                     P                 N                    Q              Q                 Q                     $J                 YQ                 ZQ                 J                  \Q                 Q                     P                  P                     DS                  Q                 [Q              Q                  J                     P                  aQ                     \                     N  
   <: F    t           Q                    @                 O              S                     J                         5  t   t     K            L     PF     I            J                 Q                    Q                 \                 Q                     Q     E ( 4    q                  [                  Q                 /[                 J                 Q                          C     C        M =         Q              C 8D Q             yO        [     > |B          $ TB pB     oQ              E     Z                 S                 Q                 ? P                 #Q                   
      ,              9 Z                  +]     ʸM                                  9       TA 7         M                                  <        7 dA         M        N                                  <        A 7         M                                  (        tA 7         jO  ,   
               3                   J            $          =                      6          :     5  t   t     #     t     Z              JUU*           t: <  <  M                                  <        7 7         M                                  (        7 4A         AP               ?   Q  
                            \     $n G          $             N     9 x>    x>     N                 Z                        M     P7 7    MP        N                 @   N                     8     x7     M      N  
                    j 6N                                  9       8 8         nN                     X:    H8     P                
N                                  9       8 8         X                                  <        ` \8         N        /N                                  <        8 @8         N     |8 x`     M     9         Q  
                     PN                                  9       l9 8         eN                                  <        9 h9         N            PN        O  
                    t: O                 
O  
                          O                 O                     O                 O                     O  
                        O                     O                 i O                 O                 O                     4N               O                 O  
                       O                 O                 O                  O                    O  
                           O                     O                  O                 O                  'O                     +O  
                   `      O                     	O                 (O  
                       $O                  O                  !O                 "O                     #O                 )O                     %O                 &O                 *O                 3O  
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         	                            ز ˸p	  	  CN        ,O              O                     M  
   9 t    9           /O                  0O                     1O                    2O                 nO        t                  $               =         u                   $                           iO  "      0                      <              =           @W            ø  =                                     I  
               o;opM  4   P   9 d   8P   D: d      $    h]T6                  $                    6	                            $                            X6                            M                       OO                 N        t           = : $               8:     9 u                   $                           N        ,              cke.m       gO     Pn =          $             kN                >                                                 >                                                 <                                                 >                                                 >                                                 >                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;    sN  "   x= p= \= =  = L= @= 4= < < < B m 0C 8C ,N M  ' <' PC LN hC `C tC xC H4 C C TC C    N  :      q                            +   ???                                                   (;         t                         Z                                                                  N         n                              (;     < j A d; 7 6 ;            :         u  7             <N        M                  $   vN     <9 9     N           *y[9N                    MN        6 Q                 N        )                             X: 9 eO        rN        EP        M        %]                                  t       0: 46         N                O                     YN     9 9     N        !N        O         hn    t      &X               O                     O                 &  O                 0'  O                     oO                                                                      _N    4˸   P          ;           p; ܠ@      P      !      `              p                                                                                                                                                                    0          @          P             `             p                                                                                                                                                      0            @             P             `          p                                                       <                                                                                                 0             @            P           `             p                                                                                                                                                    0            @             P            `             p                                                                       `                                                                             0             @             P             `            p                                                                                                                                                       0                         M     6 8       '_                 ~O        OS                    Q                    J                 Q                    Q        Z        %         I        Q                 	]                 P  4                   F      *     D D  D D     hD dE d( pE lE D C             C hE         F     ( E     C     r * p* ((     C tE ,D <(         E $D     Q  h                   PD                                                                 E                     PD                                                         \* t     D (D             PD                                                     @D D     E |E                 PD                                                 E r     E E                     PD                                             E t     : E                         PD                                         E         E )                             PD                                     $t =     r L                                 PD                                 G X}     0n D                                     PD                                 u     E r                                         PD                         l hG     ) |:                                             PD                     l? |     8; Hm                                                 PD                 > *     M TG                                                     PD              @ `E     xD ,@                                                         PD         $G &     xE ?                                                             PD     > E     E ,                                                                 PD = E     E (     Q         CB<@Q        t           N ; $       XB G -     , u                   $                           J              07 $j PK                 MS        t           C DG $       C \G Tt     H6 u                   $                           ]              @                                                                                        ʸP        Q                 R                                  (?       L? '                 N                 Q                    Z                    M                 @? 
                 J                 Q                 Q              Q              Q                 J                     J                  Q              Q                 |M                     }N  v   ^     X_ L` $_ $` \_ ` _ p` h_ X` l_ ` 8_ ` p_ ` (_ P` |_ ^ _ (` L_ ` _ ` <_ ` _ ` _ ` `_ ` _ T` @` ` ` 4_ ` ` ` ` t` a ,`  _ <` H` l` `` \`  ` ` ` _ _ 8`  ` D` _ 0` _ 4` ` _ _ _ _ `     _ _ _ _ _ _ _ _ _ x_ _ _ _ _ d_ _ t_ _ _ P_ |` h` ` ` ` ` ` ` ` $ 4$ 0$ ` 5 ^ _ _ T_ `  _     N  "         H f     0   _     g        ,O     h        9     i     0   =     j        p9                 N              @;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;                                                 ;     P                                     $                                                               P  
                         P         t                  $       TB pB (         u                   $                                   Q                     'K                  4?        E $ Q                  	Q                     -Q                 Q            Q                  M        S                                  <  r   r   0_ ,_        S          DX                          $     $ r   r   $O O         N  "         H f     0   _     g        ,O     h        a     i     0   =     j         :                 AX                 2X                 I                 0X                 I                     >X  
                  4$     I                     ?X                    [N     9    6 )X                 ;X                 :X                 5X                     -X  
               `     9X                    $X                     6X                     (X                     /X              X                     4X                     X                     1X                     #X                 qP                                  (        B 7         N               %X                 ,X                    M              YP        M        %       *X                     X                 X                 X                 X                     X              X  
               ` `     X                  "X                 X                     !X                  X                 X                  W                 X                      X                 ` X                     X                  W                     	X                     X                 
X                     X                 X                     X                 X                     X                 X                     X                 W                 0$ W                 W                     W                 T` W                 ` W                 `` W                 D` W                 _ W  
               _ _     W                 X                     X                 W                     X                 W                     FN     8 9       X                     W                     W                     5N                      W                 W                 W                 W                 T` W                  W                 W              D` W              _ W                 W                 _ W                     W  
               _ P_     W                     W                     W                     W                     W                     W                     W                     W                     W                     W                     W                     W                     W                     W                     W                  S  v   ^     X_ L` $_ $` \_ ` _ p` h_ X` l_ ` 8_ ` p_ ` (_ P` |_ ^ _ (` L_ ` _ ` <_ ` _ ` _ ` `_ ` _ T` @` ` ` 4_ ` ` ` ` t` a ,`  _ <` H` l` `` \`  ` ` ` _ _ 8`  ` D` _ 0` _ 4` ` _ _ _ _ `     _ _ _ _ _ _ _ _ _ x_ _ _ _ _ d_ _ t_ _ _ P_ |` h` ` ` ` ` ` ` ` $ 4$ 0$ ` 5 ^ _ _ T_ `  _     W                     N        W                  W                     W                     W                 W                  W                     W                     {N                          $     $ r   r   9 :         yN  
   u 9    <           W                     W          W                 W                 W              l  fN                     X:    A     N                 N                                  <        `8 P8         'X                                  <        ,8 A                         N                                  <        8 x8         +X                                  (        h8 8         N                                  9       7 0B         N     9 @9 \9 $9 8 8 (8 X8 88 08 A 7 (9         N                                  9       8 T8         M                                  <        A 48         N             N        ,              cke.m       W  v   
         	                                                                  	                                                                        	                                                                  	         
                                                                                                                            QO                 FO                 TO                  O                     P                  P                  S                      C < N                     (C 4C <C pQN        5O                 MO                      P< < < < l; ; = <= d= D= (=     P  
                   B     P  
                        KO                     P                  P                     P                  P                                          M                         P                     I                     bO                  UN        :O                 P                 P  
                          VO                 dN            T  9O              $<     (< $= l= P= T= 8= 0= <  = < l<   EX                 lO                     ZN        S                  P                     I                 P                  x[                     BO                 -O                     I                     I                    ^N        P                 EN        =O                 P                  P                  P                     4O              <     L< = = X= H= < < B B N B   P                      < C a     = ,C         @C DC HC     P                  I  
                   4C     p[                  P                 gN            $"  I                 S                  7N        P              p=     < B B < ,= B \& B m C C %  wS              a     <                                         ˸P                     P                     P                     S                 P                  P                     I                          <                                         z[              =     < B = < < C 8' N C $C ' \  P              n     < =  C     C =      C ' m &  -  P                 P  
               pC         sS                    P                 P                 P                     P              hC              <                                     S                 jN        M     # :    (;     P                                  '                                 P                                      <                             I                     P                                              '                     S                                  B     HN '                    M                mN                     X:    8         6  P                 7  M              >                                 |C             L9  P                 9  P              PB                                     C         `;  P                 ;  N         P              0                                          pC        P                     P              p                                          lC C    P                                                            C    oN     ˸B C                       d                                             x                             (                              <                       B $H            pH      D>             I         B ,         & I  @         I  @  T  T>     Hh            |      ئ˸              4I                 8I                  `    ˸          `              H    DI   0         HD  HI          X         l                                     ˸                 ˸                \I                   ئ                       ʸ   4       H               \       lI   p               pI                                                          `  ˸                              H$  I          8      IL                `      ʸ   t          H                   ˸                            `                `    ʸ              (            <       L   P            d             x                                               ʸ         H    L                H   M                ,            @            T          h  \       |  H    M                                                                 ˸              `                 @    0             `D  M          X          l                                      ʸ         H    $M              H@N  B                                    X6 ,  4: pu             # 9                         ,,:                                         L:                                                                                         xN  4   (   $: d   hf0   |9 d      $    :                  $                    6	                            $                            9                            N                       IN                                  9        9 9         N            }P                        fO  *                                                            	                                              
              
              \N                       u   =     =       9 9         C              ?   SO              `      < p< |<     d< H<         \< D< X< t: 8O                  <                                             AO                 6O  
                      ʸ^O                                              h< <                 I                              $<                     LC XC \C     \O              0                <         <                     WO                             <                     <         `O                      < <                                     ʸUO                    NO                 P                 N     q         DO  
                     LO                  <O                 RO                 ?O                  P                 7O                 P                 =N        @O                 >O                 BN        PO                     t< << 0<     < T<     8< 4< ,< @<     HO                     < < <         <         < x< `<     IO                  [O                     LN        JO                  ;N        dO  
                           :N                                  9       8 8         cN                     X:    `     'N     9         &N                                  <        8 _         *N                                  (        t8 d`         $N        2N                                  <        8 9         X            YO                 N    $˸                   ;           ; d   @      ? x   p      ? P         ? (   0      ?          ?          ?    `      ? (         xk <         `?           :                 :          ئ                         0     :     @     @P     :    `     ئp                            :          @     :         ئ                            :                 :          ئ@0           @            P     :     `      `p     :         ئ                            :          `     :         ئ                              :            0     :    @     ئ`P           `            p     :                :         ئ                            :               :          ئ                         0     :     @     @P     :    `     ئp                            :          @     :         ئ                            :                  ;          ئ@0           @            P      ;     `      `p     :         ئ                            :          `     :         ئ                              :            0     ;           ئ`N     ˸                                <        pʸP              ئd   E          x                      ;                    ʸ(;    ;     ئ                                                      p    ;              E,                @              ; T          @h  ʸ       ; |  ئ    E                              $;                p  ,;     $;       @                                                   pʸ0             ئD  E          X                  l  4;                   ʸP;   4;     ئ                                                   p    D;              `E                               D; 4           H  ʸ       D; \  ئ    Ep  \;           d       $                          $                  F                                                                      $          p8  ˸            L                  `                  t                                                                    P  E    Y Z   L          x;          h;               ˸P             `      (  <         Y <          P         [    d             x                                                                                                       <  @    Y     P              4\ ,  p      8@               T              h                |                          Xd                                  Y Y          0            @       \             `      d   0               D               X  tY            l        \d4˸                 c                                   Y Y                  N                                  (        L8 7         JN                     X:    8     N     (9         NN                     X:    |7     M     89         N                                  9       8 7         yP        N                                  <         8 <8         N                     X:    7     UP     p8         mP                                  9       7 7         M                                  <        7 7         M        M                                  <        $8 A         iP                                  <        8 7         N                                  (         8 7         M        M               8     O  
            `-    ԹN                  N                 M           JUU*JUUN           *JUU*O                    pN        N              GN                     X:    8     >N     9         hN                     X:    t9     N                 @   N                 N                    J                         5  t   t     K            SN          N                 M        M    ʸN                     Z        `    ʸN                    N                    %N  
       (;    ?          E]                N                    mO        N        TN     9      W  "      0                      <              \ *          @W   "          mo _                                     ;W  .                     
                                                                       !   ˸L   
       B          K   	    g    cO  .         $          J       o                  p        u     m        \6     q        Lu     r                        $     s        u u N     "       M        M        W  j       W          X          Y          Z         >          \          @          ^          B                  D                  F                  H          ,                   K   	       L   
       M          N          O          P         4          R          S          T         8          V          Q      !   U          [          ]          r          J                     dQ                 J                  \                    ]Q                     P                  
J              <  cQ                  J                     J                 XQ                 \                 kQ                     rQ                 ']                 bQ                  eQ                     \                 Q        t                  $               ?         u                   $                           I                        O                                          ,   O  
   , G C ? t: \? O                  d?        + $ O                                  <        xk D         O        v              $ ,n G                                  w               Q                 K                 O  
               ? ? N                  C        F $ N     J         dO                 Q  
                       Q                 2J                                                                                                             I  
                       [                 Q                 P                  =        4} $ zO                                  <        % =                 ~I           @S     , G F ? P                  @[                  O  
            I   O                  G        E $ Q                                  <        XG t&                 
Q                 sO              =S                 P            L]     "f148 (this will take a while!!)"; N  
   qEigenform(D148[2],600);                                    A            ]                 
  V                                                             
                  : Q                       t           N     ʸ[_      M                                  F       6 l}         p\     ʸ`}     \                 F[                  C     D x( 4> G hM |( '     G ?  m     C G C = = |= h= t' Q         $             .               $ $              #      P$ : q D 4D P ? ;    $         X_                       u   t     t         l: ,r         /]     $˸\         J                       u   t     t         t `r         pI     ʸQ         R         P                       u   t     t         q H         __     $˸P         vQ                       u   t     t         |} C         =_      ˸J                 P                       u   t     t         % G         M      ˸Q         Q                       u   t     t         7 $F         $_     ˸\         (K     ʸF    Q                       u   t     t         | 4+         _      ˸Q         J                       u   t     t         || XF         Q      ˸Q         Q                       u   t     t         F hF         P      ˸Q         Q                       u   t     t         C F         P     ˸Q         J      ˸P                 fQ                       u   t     t         | r         !Q         O                       u   t     t         , D         \      ˸Q         vO                       u   t     t         s 0F         O      ˸P         Q                       u   t     t         ? C         "_     ˸QB                  4F    $                P LJ                       u   t     t         xB lD         xO                       u   t     t         * dB         I      ˸M         <K                       u   t     t         `& 6         O      ˸sQ         Q                       u   t     t         ? E         =P     ˸O         J                       u   t     t         @  ?         |Q     ˸M         }\                       u   t     t         E  7         M     4{ `} * B E C dF xF + F DF E  > = 8F 0) = , G l* q tR    T                       u   t     t         | D	         =]  P                  3                               
                      $          $          t     )     u     -  t   j     +  t   j     #     L7     ,  t   |B     4     H     $  w   Lr h? %  t   t?     *  t   |B          >     1     x6                                                            d	1|                TA A A A \A `A ,A LA lA 4 |A A A A DA  A PA xA 8A     (A hA            ~Q              F pD M `D F o l P, 0r D XD k N C F + `+ F F     F F   P  (   	               J                         5  t   t     K            L     pG     I            9  u   m ,n 8  #  T: 4F jh  
               ;o                        Q                 F + F } + L+  F |  F \Q G * H+ LF ,F E F (- G     ) F F                     Q               < @ t@ p@ 0} \@ X@ T@ P@ L@ H@ D@ @@ <@ 8@ 4@ @ @ ) <?     8? ?     nR                 \     ʸQ  
                : `L_                    E_                    J                  J                  Q                 :_                 Q                     WT                  Q                 J                 J                  Q                 Q                     yQ                  Q                     JK                 Q                  FJ                  Q                 Q                    CT              'Xb b 8b b a a a a a a a a a a a a a b b     b b    oX                     yY  
               ;o    Y  
                     rX                 d d l n N d N d xN N m N N `{ pN LB N  O z     z d HG X                  $i h  i e h i h h ,i h  i h @i h Ti Xi h h h     h h I O                 O              O                 AJ                 P                     P                  P                    P                 P              P                 P                 P                  P                 P                 P              
   P              P              P                  P                 +P                 _                     x  
                     9                      o                  ( ` X h @ T | t  ,  4 \ l  H     0 D            Q                 d  d Ld Pd Td Xd c `d c c d  d $d c 0d 4d d Hd xd     \d @d    O              xa I / / 0J I I I / I / I I I  J J I I  J l/     / (J ˸rf  
            
   ;o    K               Rؒ (  ,  l d T $  0  X  L  Ԓ  В              0Q  
                            rI                  2 + + + + L2  s 2 , , @2 + + t2 (, + `2 d2     + X2    X                 tX              uX              vX              
   wX                 xX                    yX                 zX                  {X                 |X              
   }X              ~X              
   X                                      X                 X                 X                    X              X                                  X                 X              X                    %P              pe e Dd f e $f f (f f Lf e e e f e f e e f     e pf . T                9 $: 9 t9 9 4: 9 9 9 |9 ,: @: 9 : 9 L9 9 9 :     9 \:     @    
            8  ;o    N                    ]              g @W ] W ,] Y xW \ ] 0W  ] \ \ W tW d TW 4Z Y `W     W \ <a i                < l ` \ p P  ,     t $  | 0  4      T            tY              @ N 5 O N N n 5  a O O k k m k N O (l @l N     Xl N G Z                  q s s t t xt s t r r r r  s r Hs r r s r     r r     "4FY                    V              |1 D1 h1 1 0 1 0 1 01 1 d1 ,1 0 0 0 (1  1 P T1     L1 1 <  X                 X                                      n                 D7X                  Y                 Y                 w                 Y                 X                    Y                 	Y                                                       Y                    Y                 q                 S                 <Y                 G                     Y                 Y                  Y              
      Y                 Y                  Y              Y                 Y                 	                  Y                                   _                     >_              (   ^                    #_              _                 k                    MT              >   pR              ]                    K                 )                    	                 tR                 uR                 K                 vR                 wR                 xR                 U                 K                 zR                                                   lk}R                 K                 ~R                 Q                    R                 X                     r                 R                    R                 "                    K              R                 K                 R              
   
                    K                 S                 S                    S                                     S              S                 S              
                                        S              S                 [                 [              \                    S                    [                 
   #  
              ;o      
                 ;o    Q                 *Y                                                          P              #Y              8Y              
   (Y                 4Y                 l                    ^                 ^                 ^                 [               ,] ^ ] \] ] Y \} ] ] ^ ] ] ] ] Y ] ] ^ ]     Y ^            [              ".| | t| \| X| Q d| |  | H| 4| D| | P @| pP 4Q P |     DP |      a              .        $ Ԃ  Ȃ     0          t- gY                 iY                  ~Y                               T   zY              Y                                                   qY                 sY              i                 wY              
                                         xY                 r                    |Y                    Y                 Y                                                         Y                 c                    Y                 Y                 Y                 Y                  Y                 Y                 {a               bC4 ئ   Ȧ , ( L     8  ̦ T  Ħ       @            =K              >   `f                 D  $        8 (  4  0         ġ    7Z              *   &Z                 3Z              W                    'Z                 <Z              $   C              
   8Z                                     ,Z                  .   '                 0Z                 m                    /Z              &   o                  p                    5Z                 S                     4Z                               KZ                 \  
               ;o                         ;Z                 PZ              @Z              UZ                 
   EZ                 T                    IZ                 VZ                  HZ              *   a                  $  0 `  D <      X 4 H l 8 $ L      ,  aV                  @_                   
            @  ;o    Ɠ               S D S S S S T S S $T S S S S S S S S S     S S                          3  
                      4                                $  P ( d 
 @ 
 
 \ 
 8 
 ` 
 h 4 X , 0     l D    S                 `                    [                 V              s $ $ d% l% $ T% @% $ $ H% $ % 4% % ,% % 0% % %     <% % uV  
            h         
V              U                 V                 5 6 5 5 x5 5 $$ @ ($ ,$  6  6 5  $ 0O $6 [ 5 @     5 5     [                 S                  [                 a                 
[              <   S                    Z              6   Z              0   S              S                 S                 Z              4   S              bM              2   @X              "   pM                 S                                  q[              S                    _                    S                 M               % L 8 T  $ |  P p  ,   h H X \  x               \                 aT                 S              J, , h, , , p, , x, , , D, \, , H, <, `, , 4, ,     , @,     W_              B   T               " W W (X W W  } W W W <X DW W W W W W  X X W     W X         \                    \              2   \              6   \                 \              R                    \              \              K                    \                 >                    \              \              $   \                                     ]                 \              :   :]                 \                 >   f                                      a\                 =                       "]              $   \              :   \                               !]                    :d              (T   ` d  @ 8 $   x p h    l \ (     <      ~c              X 4  `  ș X < Й H 0 L  P  \ @ ԙ ̙        _              _              :   :T              :   _                 S              &_                                     T                 2_                 _              8                       /T                                     _                    _              >   /                 T                                      _              &                                         lk _              %   _                  U                 .F                 V                 >   7W                  %W              >                       kV                                   EW              ,   e                    ?W              <   @W                 DW                 lV                  KW              &      9W              D   2Y                    U              U                  U              0   U              U              .   gW              .   o              l               2    x d `      <  l @ \ $   X     4 h            -T                 K                  4     H      D                 n               BY` p  t @   l   l 8  4 |   T                  N                          `	   iW              WW              (      lW              (      :                    `W              D   qW                 rW                 H   #                    sW              L   P                    vW              fW              :                       |W                                  xV                     cV                                  ~                 tW              W                                  W                  W              *                       W                 pV                                                       L~W              .   U              &   &   V              *   V                  U               V              V   U              2   h                    U                 U              F   U              0   U              N   U              v                                  $)U              "   U                    U                 U              F   U              *   U              R   U                     P                  U              <   U              U              U                                 ԋ          ؋    ċ  $              @  a              p   ~a              R   b              r   j                    b              g                 b              zL   a                 x                                        Lg`a                                     a              d   a              b              F                          b              J   0   ga              4                                        db                                  b                                  b              P   b              "   q                    /a                 0a                                  a                 a              6      a              t   %f              xD   Om              Ї                 D	  & & & & p& L& & & & d& <& & X& t& P& $& `& H&     4& h&    .K                                                       7K              `   *K              *   .   5K              <   a  
               ;o                        0K              K                 -K                 W                 +                    K              \   K              P   	j                                     j              t   j              *      j              
   h                 j              Rp   j                 j              F                       j              "   j              l   <                        !                 j              j              j                                  j              j3                 !j              R   
                       #j                                  %j                 ^                                      (j              x                     *j              4   +j              q      S                    f                    	I              X   9P                                     7P              :   M              X   F                 M                 I              ^   
I              8   I              
   M                 nM              M              Z   M              4   ~M              5   eM                 vM              (   0   iM              oM              6                    lM              ^M              ~              Xt0 8  $  D L 4 (  H     \             L              0   L              J   L              L              B   L              2   \              D   
K                 J              <   *   7                    J              K              `   J              K                 J                                     J              Z                       J              L              \   J              0   4                     J                  `   a              t   x p 8   @  T  < ( X  0 , <      \    `h              g  | ȧ ا ħ    x d ܧ  ԧ  t l          X jm                 t |  D    l  L p   ľ  0 $ T  8      4  9f              D   0   ށ              $       T      0          ,      L       8   ʸ`L              lL                                                    lkZL              n                 UL              #   bL              $   LL              <   _L              ;      QL              :   YL              b   KL              J                       BL              <   Z                    (                 SL              
   >L              JL              =L              Z   HL                 R   4L              &      EL              8   "                    )   u                 .L              P   c                    a                 |?L                                 0   |   8 H   <   h   $       L X     j              j   #K                                     !K                               K              <   K              2   l                     g                 ; K                                     K                 K              K              Z                       K                    K              d   K              8     
              ;o                  p   b                   D D XD D DD N D D \D D D D D lD D <D D xD D     @D 8D     @  s                 ,          ` \ P            <     L              &      d  
               ;o                        L              iI              "                       b              b   da              D   4y                  d ( 0 x @ \ T   |  `    X H D h     p l     Gv                              , $         |             x              tR  fI              4   YI              .                    OI                                                       `I              n   KI              0      k                 Y                 [I              F   (   UI              [                 RI                                  PI              l   <I              H   MI              ?I              N   LI                 l   FI              2I                 CI              ^                       AI                                  
   >I              P   1I              B                           -                    :I                 1              \ 	̚  8 0 ( , Ț D Ԛ   H ؚ $y      4     ܚ < *              P DQ lQ P P P  Q P Q P @Q (Q Q xQ XQ Q P HQ P     ,Q P    r  
              ;o              d   L                                                        <                o              V  Pt              Nu              :
   y              V                    {              P  |                 }                   ~              dv                                                     :              t                                     z  j                                  :                                  \                 h                                  4 ܃ ȃ  p  Ѓ D 8    @ ă ̃ <  ؃        /sf                 tf  
            p           w              `In                     d              "   t   d              Y      k  
                   `              (   p                                     4
`              J   -                 `              P   `                     `              D                       `                 `                 `              x                    `                 `              :   8   `              B   `              D                    j                 `                 `                                     y                 lk`              L                                        .`              ~h   p                    `                 `                                `                                  `              t                                         |`              `                   h p 4 $ Ȯ  l  Ԯ , Į    @      (             "              :                         (                 x    Jt                 b   c              s  
                    s                     d    T L t h    l x   P                 [m              T   {                h p <  `  d P x   8  ,  h $ 0      X \     @    
                      44                   ;                                 | P  x L t   `  < (  T  d 4     \      c                 ~^                    m                     c              V   c                                c                 c              @   H   {                     b                    c                 c              R   *                    c              6                     c              \                    T                    c              n.   c              &   $   c              S   c              \   c              c              "   Pc                 9                    @                 c                                     c              X   +                    c                 c                 b              X   p   b              :      ^a                                  \a                                   Za                 [a                                         Wa              D   Ua              f   Oa              r                 Pa                 2                 Na              `   N  
            R;o    *              Ja              b                                     Xa              V   <   Fa                                                   mCa              
   ?a                 p                    b                 b              v   h              "P T 0 d d   8   h @ < p X L  H D (           d                                  d              
   d              j   d                                  d              v                       d              <   d              $                    d                                  d                                   H                 Dd              \   d              xX   d              X   .   d                 d              B                       d              `   d              =                                     l#d                                     d              i              8   i              .   i              X                          i  
            6t                         XI I |I \I I I I I I I xI I I I dI I I PI I     I I                          Fi              *                       i              V   i              z   i              i                                  i                 Hi              i              p   @   i                 i                 >                 /                 \Oi                 i              0                    i              j      i              J                     i              N                                     di                                     i              L`              ꤏ  ԏ ؏    ȏ  ,     $           ď     s                d           Y                                              l     ȯ          |     O          Ѐ     tN                  Ԁ     H                       4     P               }             L     ,L     0L     X             K     {     <L     K     ,                          ؘ          T     (L             T          K             dL     K          N     Ԙ                            .     l!          }           <               d     Ę           p                       ܘ                                Њ     (                  P               $     h     `     ,     L!                  t!                       0     D     !     0!     !     8}             p     !     T!     !     !             L     !     P     x             |     h"             h          !     4"             L"                  3     t     8"     "          "     x"                               ԙ     #          $     "     4     !     3          "                     3     "     "           #          ̙     ,#                       3             4     3     ؙ     d4     3          P:              4     4                            P4     3          4     7     3     ,     p4     ,T     0     4                  9                   5     (     4     4                  4     @             8             D     8     8     @8     $5     t      L      8     4     8                   <     08     5          l8     x     8     D8                  8             |     8               8          <9     8             x8     8                   H9     9     (y     9            9             :             :     l      9     p9          9     l9     @9             9     0     <      9     9     :      :             $:     9             H      \:     ,:     H!     H:     :             x:     |                            ;     (:          !     X:     :          :     :                          :     ;     \     :     ,;             $ $                   _ _ _ _ ` _ _ _ _ ` _ ` _ _ `  `  ` _ _     _ F     g                 uf              J   yf              `   r   ~f                 f              f                                   f              f              <   .   f              \   f              B   f              @L   !                    f              r   f                 H                    f              f                 Zf                                      f                 f                 ,f              V   T                 (                 nD                                  T  b                                                r                                       4                 `Ԃ                 Â                    ʂ                 ti              r   i              Xl   i              0   i                 i              i              J   ?                     [                  i              &      i                 di              m      1                 i                 i              R                    3                 	   i              i              l   :   i              n   i                                                         i              p   i                 i                 3u              N   4     D       (   $            kh              4R   lh                 (                    nh              J   J                    E                 Dqh              Z   xh                    o                     zh                 {h              
   .                    }h              
   ~h              h              z   h              `   R                       h                                  h              z                       h              h                 NI                    h              h                 h              >   V                    Q                 lHh              f   n  
              ;o    ļ                l  @ L D \  p   P H    |              @  B  
              ;o                  X                   "                 "   ,                                  d              rV                                                                                  ^  \              r                 p                  z                 &                &                                       N                                                   t                 pB                PV V U U  V <V U U dV U U 4V V (V `V U $V V U     TV XV     @  v                 v              
   n              B   n              ,      y              2 P3 2 L3 2 3 3 2 2 <3 2 (3 D3 H3  3 83 t' 3 2     3 3  ˸i              %                 i              n                 i              H      N                8  x  d  \  D  &   @ H T  P Ժ     к l     @  v              n              n                 n                 n              H   n              h      n              R   n              *   n                    n                 P   "                    n                 @n                 n              Hn              &                       n              n                               n              x   n                 d                 t tw \w w w w w Hw w w <w w 8w w w Dw w pw Pw     w xw                        2|               X   H  p |   `  0 D T d @ ( L  8     , <     Iu              ~   P   _u              B   Z                 	   au  
                                 f
                                  ^j                                      &                                  .3                 	              D  
                 >              H                 X                                   n    
            ;o    =k               \u u u u u @u Hu u u Tu xu lu $u 0u m u `u Lu (u     |u u                      Y              Lr              r   ^                 p                                   L!                                 d    (   ,  D   0 @ T 4              @  6               bl d7 p0 @8 8 8 l7  7 0 7 x7 t7 t  8 0 7       7              
                      9                  t                                   R d -  P  H   (    8     \      D      B>	 	I                          u      f  
            ;o                  B	 E D D E D D D D D D W D D E D D D D D     D D     U                 > 8? > > $?  ? > <? > > > > ? > ? > > ? >     0? >    r                     0        $ D    ( ,        L        <  p                 Hp               bH     x   4   l \ @ <  L h      T P     2v              r      :l              F   ;l              `   'l                 xm              l   ym                 ~m              @                    f   m                  m                                  m              x   m              d                    m                               m                 m                 Dm              
   m              x   xm                m              2   B   m                 m              *2   m              z   I                    w                 m              m                 )              m              Al              Bl                    Hl                 Il              LZ   9                    Kl              Ll              t   P   Ml              Nl                 <Ol              z                       Ql                 Rl                 Sl              Z   il              @l                 Vl                 T              Xl                                  s                 [l              H      }T              2   T                 O                          ]L	   U              "B  p              p                 22                    G                 \Op              H      p              `   p                                   |                 p              v   V                       p                                     p                    p                 p                 p                 *              $   p              D^   p              v   p              p              p                 p              <   p              j   A                    p                 w                 l   x                   t             w               d  p  t (     , 8 $   l 0        h             p              r   p                 *                    p              vp                 b3  
            *   ;o    p                                                      dp                 p              B   p              h   z                       p              @   F                    p              >   p              $   ~                    p                 p              x   p                                  p                 rp                L                  p                                   p              p                 p                 Q                    r                 2M                 N   t              XKt              Lt  
            t           Ȇ                                 Բ l    0  h T `   P 4 X < ,  \     в       @  t                 }                "}                 ~#}              v}                                     &}                 v/}              r   "   (}                ,}                                   :                 |,	D}                                  1}                 ~                    3}                               5}                 z   6}              <  n7}                                    @   N}                 j8}              |  9}                 :}                 n=}              4   >}              z~Mt              p   *   L                    F                    Pt              f   Qt              r   tRt                                                       Ut                 Vt              Wt              Xt              Z8                       Zt                 x[t              6                          ]t              
"                   _t              gt                 ht                    it                                  kt              F   t]                     mt                 nt                 v                 X | 8    d  , l  0   x < t       \ (    t              <   P   t              ^  N                 t                 t              @  t                 t              J              
   t              5                                   l#t                 Rt              
  t              "   rt              D   t              n      t                 `t                 t              nt                 t              N   L                 t              L                    t              hq              F                                                                       6                              P                                    4   t                 0                   "                c              `  i              v  l                 D                    _              .                        s                m              |                u                 a                                                  {              B]              H     ~                                                                                                                 
  p                                                                   X\                d                   j                               t     n                                      b   e                                               H                                                            x              `                \                                 Hn                6                |x                                  0                 z6|  
            X   ;o    D                                                                                                                 b                                x   |  ]              K     ^              T  a                b                   c              J                   e              R  f                 &   g              h  r                 ,   i              $   |                 k                $;                 m              0n              nv              p              F     q               ,   ~                 s              `   4              8  $                 "#              .  &                
                 9              b              $%(              >                     *              &   '                                        .              h  
3                 $0                 4   H                                       5              $   
M              (   $                    :                 &;              P  @              $                                  l>A              <                 ntSU              0                   	  
               
      4 -n              d    m              Y                 _l              n                n              P  n              <  n              0   aa              <  ol                                    wl              8  #n              $   yl              ,  kl              P                     |l              "n                 <   fl              $                                 F                                 R              \                                    xh                $                   `                                &                                                  r   <                                      	              \2                                    w              R  x              P  y              V  z                 <                    |                 
8                                                    8  (                ,R                |                              X                Z  }              H                                   C                                                      d4                               
   t                      d      | x    p  h                         N                                                     \|                                v                ~:                                                H                 ~                4                  Z  !              ]  "              VD  #                 $              Z                   &              l                     (                0  )              T  %                    &              j   '                 (                   )              ^                                          ,                -              .                /              ds              1                 z              3              `  4              :p                 &   6              >   @                                  \9              a     w                 4   ;              ::  @              &A                 B                C              `  D              &              B                                 @  @                 :                                  &                 (                                                                          >  <              ^  N                                                ,                &                x              NT                 m              4  n                 n              0n                 <                                    P                                     T                                n|                              :<                0                M              ,   d                    O              4S                T                V  U              t                    W              `   X              <  Y              >    
            0   ;o    ]                ^                 d_              z`              j                    b                                                    ٍ                                 ۍ              f  ލ                g                 *                 l                3                                                P                n                 3                                                     r                       ?                 [                                    ]              l  `                                                 R    
            {  ;o                                      rHJ                    ,                 <	              f                       ì                Ĭ                Ŭ                 ?                                     |Ȭ                
                                     l>ˬ                 ^  ̬              ͬ              Z`                      Ϭ              bԬ              լ                t֬                X   ׬              0   ج                                  ڬ              t  ۬              H  y              l                    y              ^  x                    y              t   sU                `S S R hS pS XS @S LS S R R 4S |@ TS \S $S S tS R     ,S  S     @    
                                       Э     $ 8   p  dZ @      D       |     F     x              <                       x                 Y                    x                 0   {              t{              .                   {              ^  k               O O O P O O O O P O O O P O O O O xG  P     O O     bu                   I                    fu              npu                 Dtu              u              hn  xu                               8F   `                                                   L                                  X   <                F$   g                                  &                \
                 p  8K              " \B 4B TB tB B B A C B `B B A XB B dB B B DB B     pB xB     k                                  k              ZO                    k              XV  b                    k              V  k              T                 \                     k                 .   k                Utk              4  7\k              $  Nk              P[                  ,k              n              N                  X                 N     e                                  t  
               ;o                    X                                     *              P               J                 t  0                 8                                               H  |a                               Tt                 | L| \| h| || l| } | 4| ,| P| | 0| d| t| p| x| <| |     | D| ݉                T  
            ;o    R                 
   ʆ              x   nˆ              t̆                7                 Ά              `φ                 tІ              P   P   ц              P  ҆                    ӆ              p  G                    Ն              ֆ                                  ؆                 ن              0F                                    l>܆              $   dY                                      d߆              ^  j                                       *                    B                 >              4                                 }                                                                                   y                                  .   4                 >                 >                                                   2                                                                                    *|                                l   d                                   6                 	              B                    <                               f              P                 :   8	                    g                                                    @                                  *(                 p   .{                                        j              >                                                   ,                 $                (  ^                                  ,   J                m               | x < t  (    4 8      p P      T                   U                                   H  p                                  v   f                                 F                                  f                                                                                                     j              TC                 N     ʸa                 "   Ŋ              RƊ                 ʊ              lB                   @   ̊                    ͊                 Y                    ϊ                 ZЊ              V"              =                4   3              ꄘ  l   t  L x |   h T   8 P              
            H   ;o    m                   ̜               М  Ĝ      ؜             Ԋ              f   Պ              v                   ׊              ؊              t   Jۊ                 ܊              <   &                    ފ              ^                                                  ^               h                  R              h   R                    M                 \                 8                 0ޑ                                 , ̕ Е  X   ( H \ ܕ    ȕ T    L     ` 0       
            j  ;o                  rt   k                @k  
               Xh~                                 @                 v                                     Ì                                     Ō                 ƌ                $ǌ                 ʌ                J  
            ;o    Ό                 ό              v                    ь              fҌ              B  ӌ                    Ԍ                 ~               x 0 t  L `   T  (   <     l t      p       
            ;o                p                                           .                            6                ~   Z                                      č                                 ƍ              dH                                      ɍ              Hʍ              u                    ̍              <(   ͍              Ѝ              \  э              P   ҍ                                    ԍ                    Ս                (֍              ,P   ׍              ^k              b                   k                    k              Lk                 k              k                 k                 b  k                 Fk                k                 LE                     k                 T                    k              r                                                               L#              @   z                     d                 "                                    (                   )              :  *              <                    ,              V+                .              n   p  /              X  j0              D  1                    2                   G              vH              :                 H   J              *   K                N              8   Q                 F   l                 S              @  T              \     U                   i                     W              Z   X              *n                 Z                 [              0  ^                 _              P  `              |  >d                   e              0Ν              Dϝ                                    ѝ                 :ҝ              J                       ԝ              ם              ܝ              6  ݝ                 ޝ              .                              R   S              2   /  
                      5                                                       \5 5 H5 5 5 5 P5 X5 5 5 6 5 5 5 5 h5 5 5 D5     5 5     @  u  
            Z  ;o    I              f  T                m                    V                W                    w                  Y              l      ^                _              `                 N                     }                 c                0                    h                    f              f                 h              ,~   i                j              "  k                d                 m              (n                o              ,   r              @    s              $   T                    u              v                (w              (  t              j   м  
            ,   ;o    e              `  h              L  @ T  x |  X t  D    \  h       d                                  D                        I                                  <                                 F              F                                                                                                   4n                    +                                 @                               ~n                  >                                                                                     s              L  t              ^              `  _              0   `              6     
                     F                 Vc              d   d              `                 
   f              F                       h              8  i              F  Dk              6Ck              4}k                 6   ?k              0  @k                 8                 8k                                         Ik              87   &k              *   F}                 H   <k              d   y                 Pk                v*k                   Qk                 8_k                 6bk              >  Gk              $    8              x	& & & & x& & & & & & & & ' & ' ' & & &     &  '                V                                 6                   $                     9                                             $                   T                "   s                                  ,                      
                 f                               4                                  :                                                                                                              h                                        Z                                     \                     q q lr  r q 0r r Xr ,r (r r r q q `r <r q q \r     q @r     @                F                p~              
                 h                                          ,                    .              6                                                (              2              ,                 T                 S              8                 F   U              k                    W                  X                                                                                                P                                                 8  P                 J                0                     
               <	(>	F              xG                    <                  I              (J              0                       L                P              2                     R                S                 6x                     U              <?                    W              9     X              t     [              ~  @C                       
                  4 7                                    X Y X  Y X X X X XX X X $Y X X X 4Y X X  Y     xX X     @                                   2                T                  :t                                  L                7                   4     {                 ,                 R   I                P                              xH                              z  '                                                   V                                p   Z              h                <  b                  ~                            j                              ,   v                               L                                                                                          &                                                                                b                                                6                   j                *                Jl                                 2  f                            J                              v                 @                      _                                  B  @   U                               r                              2Y              J   Z                               \              `                      ^              >_                `              L                   b                      
            n   ;o    f              d  S                 h              l              >  ^  o                 p                s                t                 u                v              w                x              ~  y              *   x                 %                 t	|              l   ^}                                                            h1                                                                                                                 T                FZ                                2<                $                                          \\                \              \6                                                                                    >  x                                  l  (                                                      %                                                    h                            z  6                                                                                                            \                 xJ   X                                                                                  z                                  4                                \                                  N                                                       z                  ~                            N  F              $                                                                       D                                   ,                                                  R  D                 nz2                                                   C                 +                    '                  %                                                          !                                                                                                                                                                                                                                                                                                                                                                                      t                 /   >                 	              :                 @                6                6                L                 6  L                               B  d              n"                                                                  (   5                    .                                  j  #                 R                     "  
               ;o                  (              *                   $                 t                                4z                  (I              N                O                                  =                    R              V                                        	U                nV                W              R8  X                    \                    Z              v4[              P  ~  V                 ]                ^                K                  `                a              E                 c                ^                    *                 f              z   @              	                            i              P   j              4   Tk                &              &  '              n  `+              r   (                    -                    .                /              \0              L   1              VO                     3                 4              $  7              J  8                V9              :              Lt  
              ;o      
                      C	>              j  F                G                  H                                              B              n8                 *                                   b  H                              @j                               R                                                     ^  .              l                                 p                :                                                                          h                                                       (w              P                        e              q	z                {                 L|              :   D}              ~   0~                              V              ~&D                               F   P                 "                               8\                                                       	                ;                               Z                                                 I                                                     v              >  y                 z                                    |              }                ~              vZ                   b                                                  X                (              
                    d	                  A              	                               z  ~              6                    Z                              f                <(                 T     Q              2:   R              Jd                    g                  b  G                 V              t  W              "  9   h                pZ                  ^#                    
                 	d                 a              pd                                        i              N
  T                f              F                 e                  ~              j                k                                                     n              ,                 &  r                Fs                                 `              \     Z                              |                                      o                               z  X                 j                                 i                               u              	                 j  6                    L                                             t(b                               z                                                 j   2                 "                 Tr	              0  $                               :   x              R   d                                  J                                                 \    l d  X   ,!     x             
               @                    l   D] Q R (Q R 0 R DQ Q Q 4R Q <R 0 lQ |0 Q HR  R     1 1 	              
  $                                    8   +                    4                                  f                                  |                                    8                j                                    D                $                 bn                                                  8                              b                   6                                                                 p  ݍ  
            ;o    0                                                  "                     u   t     t n   n   }                                                                                        .              f              
  *                q                               z  m                                ~                                              *                               j                      ±              B                      ı              p                      )                 Ǳ              `   ʱ              @  ˱              dz  h                    ͱ              4   ұ                 ӱ              |  Ա              L  ձ                    5  
                    4              |  p5                6              "   j                    8                9              .  4                     ,                 	<              L  =              p   >              P                                      A                 (  B                    C                k                 E              x  F  F                >u  
              ;o    1                    J              H   K                L              @M              !                     A                    P                Q              |U                    Y                '  x                 y              z                {              l              4  n                fP                                       T                a                 (                                                                           (                               F   T              H                  d                                               P  :                                .6   J                              
B                                    (              &                 Xd                 L&                2  w                                      
            T          Ѽ                Z              
   
   Ӽ                X                 $   ռ              *  H  ּ                ׼                 ^                  ټ              ^  ڼ                ݼ              f   v޼              :   ߼                              j                6              "                                   2              >   j:                Z  9                                        ;              4  J                *?                 @              |  X.              R                      R                                 G              D              "    
                       K              g              2   Q                P                ^                V              L  L   [                 b                 8   e              @   u              &                                `                                     v                |                v.                                      2              H              &  L                                                                          ൿ                p                                   *  x              Z                ,                                        6                  \  ǿ              ʿ              0  ޿                6                              ]                                  X                @c                               2   u                A                  h   |  d \ l   D ܱ     P            @                <  O              (  J              0  W                                               *                      X  d   x  `        |           @                  f                  g                    f                 i                m                `n              F   o                 T  $              	@ < 4 t  \ d    T  |  , N L   `       @G		  
                  3                                             8                                                                     @                 0  Ā              &                ̀                                                   "                    @                                                       ݀              ^     Ȁ              \                                >                                               x&                 p  <                                                                                  @                 v  "                                                  r@                <  8  *                                                             <T                                                     |E                                                A                   Z  :              <              h              z                                                                   r                l                xP                                                                    T                                 l   t              t  `                 (                    /                    f                    1                t2              b   dT              n                   L              (   vzT                T              L  [T                N   sT              <                   QW                T              $|T                 n  T                                    JT                  qT              b  'L              ^  T              #L              qL                                  QT              ,  4              5              (   v8                 9              <   =              f  >              ?                                  A              B                C                G                H              \  I                J                 K              l  L              F  T  Q              zNM                 S              p  F  
                                                  .                               
  9                         f                 0`3                                                    6              ^                 \                   S                                 /                               *H                                  z|                V                   *5                            28                                                0<                   -  
                  (# M                               f    D                 
                 n                                  &                
                 B  x                                                                        ,                4                  l                  
                    
                                                                                                                        
                            \                                  j                '                                                                 &z  	              >                  6(              :                Y  =                 +                                                                1              z                                    )                                     p              L                   "                ,                z                  Bz   !              8  #                                <   '              N                `b                F                 2                4                 B&              -                                                       x              8=                     z                @                 |              .  7                    ~              ;  <                                  f                                 4                                 F                                 x                  
                      4 5                                ?                                  F\-                                 tH                               p  	              <              .                R              v              .  <                                                 8                4                                 0                                                        b              Z   d                                l              >                   v                                  |,                ~                     (                 *              2   $                    N     save "valentine.s";                  E                              &  	           M208                0                               *  Q     M208:=ModularSymbols(DirichletCharacter(208,[1,1,6]),2,+1);   
   Q                                                                           4                     \u ;                                w                           Print(M208); Symbols                       L   p;     p;       ; l<                                L   p;     p;       ; ;                         N  
   D208:=Decomposition(M208);                         L   p;     p;       : ;                                L   p;     p;        X;                                L   p;     p;       ' ?         M                       L   p;     p;        ;                                               L   p;     p;       S d?                                              L   p;     p;       @ ?                                                                            L   p;     p;       ? ?                                              L   p;     p;       > ;                                L   p;     p;       ? <@                                        L   p;     p;       t; ;                 #                      M                                                                                       ;                                      
                                  M                               h   ;           L;          l; p;                                         (     ˸                                                                N  
            `         !  ,                                                                                                                            ,; |; T; :     ;                              0                                   
                                                                                   <;                 <        ;                                                p;                       :    X;                                                                        L         p; <               ; \;     %                                             '                      lb        ͼ                                                     L   p;     p;       x; L?                                                   ^                                                                  
                     ,                       
   `; H;    p;                                             <        ; \?                                 D 3                        $     c             d     0   :     e        P            .         $                 o               p        :     m        D?     q        ;     r                        $     s        ; ?                                L   p;     p;       S ?                               پ                                                     L   p;     p;       t? p?         
        1                                     L   p;     p;       (T ?                 Q                                            
                      ˸                          $     $       l? x               ; ; P        }      I        #                                     L   p;     p;       D 8           
      ,                 I                                              L   p;     p;       S T                                             ʸ                
                                                 L   p;     p;       ; ;                                L   p;     p;       ; d<                                        L   p;     p;       ? ?                 o                                     L   p;     p;       `? @                                                      L   p;     p;       T S         -              W                %      N      &                       L   p;     p;       R T@                               	                                     L   p;     p;       S xT                                                      L   p;     p;       ? T                                                      L   p;     p;       T P?                                /                                                     L   p;     p;       ? |?                 m                                                  H                               L   p;     p;       ? ?         =                       L   p;     p;       S ?         ]                                       L   p;     p;       ?  U                       u                       L   p;     p;       x A         h        3              }        g      v     h         	/           /                                                  ?                    w                       L   p;     p;       A tA                                L   p;     p;       S S                                L   p;     p;       S S                                L   p;     p;       S S                                L   p;     p;        @ d@         !                       L   p;     p;       8T XT                 _                             L   p;     p;       LT HT         $                                             L   p;     p;       T 4T         r        	              &                       L   p;     p;       U lT                               #                       L   p;     p;       TT DT         1              3                               L   p;     p;       T T                        "        .                       L   p;     p;       T T         )     4                 S                       L   p;     p;       T pT                               >              M        C        W              U                       L   p;     p;       \T ?                 1              m                       L   p;     p;       S S                 k                                     L   p;     p;       S S                                                      L   p;     p;       S S         	        -      :                                L   p;     p;       $T T                                                      L   p;     p;       S S         '              R                               L   p;     p;       T HA                       <                               L   p;     p;       S T                                                      L   p;     p;       PT 0T         +                      %                       L   p;     p;       T T         q        )      V        E                       L   p;     p;       U XU         Z        ;      T        _                       L   p;     p;       hU PU         X        1      J        0                               L   p;     p;       T \U                       A        U                       L   p;     p;       B A         P        +      r        k                       L   p;     p;       @A A                 U      Z                               L   p;     p;       B hA         G              X        L                       L   p;     p;       A `A         S              ^        N                       L   p;     p;       LA xA                       a        I                       L   p;     p;        B A         W              y        `                       L   p;     p;       \A A         Q              d        f                       L   p;     p;       DA A         o              _                               L   p;     p;       A |A                                                      L   p;     p;       C D         ľ                                             L   p;     p;        |D                 y                                     L   p;     p;       C D                 M                                     L   p;     p;       `D LD                 3      	                               L   p;     p;       D $D              4         3        
        s                       L   p;     p;       A B         j                               L   p;     p;       A A         |        i              g        5                       L   p;     p;       tT hT                                L   p;     p;       T 4A         ,        *                       L   p;     p;       U T         i              ?        +                       L   p;     p;       U T         F        I      ;        7                       L   p;     p;       U T         /        =              6                       L   p;     p;       T B         f        C      ^        A                       L   p;     p;       U xU         9              B        (                       L   p;     p;       T U         M              @        c                       L   p;     p;       4U  U         8        /      0        L                       L   p;     p;       T T         2              G                               L   p;     p;       T U                       N        D                       L   p;     p;       B 8U         K              R        P                       L   p;     p;       ,U HU                 '                                                                  о                               ƾ                                                    t              q        {                       L   p;     p;       A A         b        \                       L   p;     p;       `U (U         b              l                       L   p;     p;       U @         O              I        Q                       L   p;     p;       <U $U         e              Y        g                       L   p;     p;       U dU         `              n        U                       L   p;     p;       U U         <        9      k        ]                       L   p;     p;       @ U         [        -      a        n                       L   p;     p;       lU U         c              -        l                       L   p;     p;       A @         h              o        i                       L   p;     p;       U U         J              '                               L   p;     p;       (A @         K              ,        D                       L   p;     p;       ,A @         6        O      d        m                       L   p;     p;       @ U         3              (        [                       L   p;     p;       @ @                 q      j        7                       L   p;     p;       xR U         E        !              &                       L   p;     p;       A HD         >              .        5                       L   p;     p;       @ @                       C        9                       L   p;     p;       R A         O        ]      4        "                       L   p;     p;       <A @         p        K      :        =                       L   p;     p;       U @         2        7      8        F                       L   p;     p;       @ @         T              Y        ?                       L   p;     p;       PA dA         V                                             L   p;     p;       XA B         H        %      ;        1                       L   p;     p;        A @                                                      L   p;     p;       B C                                                      L   p;     p;       $C hC                 )                                     L   p;     p;       C ,C                 =                                     L   p;     p;       C  C                 ;                                     L   p;     p;       B (C                                                      L   p;     p;        C HC                                                      L   p;     p;       8C C                 )      ?                               L   p;     p;       C <                 e                                     L   p;     p;       C TC                                                      L   p;     p;       lC DC         0                                             L   p;     p;       < C         >                                             L   p;     p;       < PC                 ?                                     L   p;     p;       C D                                                      L   p;     p;       C dC                                                      L   p;     p;       C C                 !                                     L   p;     p;       C C                 9                                     L   p;     p;       D C                 K                                      L   p;     p;       C C                 -                                     L   p;     p;       C C                                                      L   p;     p;       C C                 +      R                               L   p;     p;       2 H-                                L   p;     p;       C <                 5      |                       L   p;     p;       <D (D         ;        O                                     L   p;     p;       < TD                       y        S                       L   p;     p;       4D 1                       W                               L   p;     p;       XD ^         %                                             L   p;     p;       < |<         8        	              B                                              L   p;     p;       A 0B         e        5                             L   p;     p;       A A                 #      \                               L   p;     p;       B pA                                                      L   p;     p;       XC HB                       z                               L   p;     p;       lB A         p        W                                     L   p;     p;       A B         x                      ~                       L   p;     p;       A B                                                      L   p;     p;       PB 2                 Q                                     L   p;     p;       $B hB                 I                                     L   p;     p;       2 4B                 {                                     L   p;     p;       B B                 	                                     L   p;     p;       h< PD                 	                                     L   p;     p;       ,B dB                 C                                     L   p;     p;       8B tC                                                      L   p;     p;       C 0C                                                      L   p;     p;       `B t                                                      L   p;     p;       B 2                                                      L   p;     p;        B B                 s                                     L   p;     p;       C B                 /                                     L   p;     p;       LC B                                                      L   p;     p;       B C                 G      ~                               L   p;     p;       B 1                 _                                     L   p;     p;       C B                                                      L   p;     p;       B B                                                      L   p;     p;       B B                 ?              U                       L   p;     p;       `2                                                        L   p;     p;       2 <2                                                      L   p;     p;       @2 42         }        a                                     L   p;     p;       1 2                 +      ھ                               L   p;     p;       2 h                 %      U                               L   p;     p;       82 T                 M                                     L   p;     p;       d2 P                                                      L   p;     p;       D2 1                                                      L   p;     p;       T2 l2                                                      L   p;     p;       |2 2                 	                                     L   p;     p;       H2 2                 U                                     L   p;     p;       2 x2                 c                                     L   p;     p;       t2 ,2                                                      L   p;     p;                                                              L   p;     p;       L2 |         ž                                             L   p;     p;                                                              L   p;     p;       T 2                                                      L   p;     p;       2                  a                                     L   p;     p;       2                  Y                                     L   p;     p;        2                                                      L   p;     p;       2 |                                                      L   p;     p;       2                                                       L   p;     p;       0 2                 S      Ӿ                               L   p;     p;       ( L                                                      L   p;     p;        2         .                                             L   p;     p;       8 2                 Y                                     L   p;     p;       # L                 E              +                       L   p;     p;        $                 S                                     L   p;     p;       d <                 3                                     L   p;     p;       h \                 E                                     L   p;     p;       4 #                 g                                     L   p;     p;       P                                 Ͼ                       L   p;     p;        2         ؾ                                              L   p;     p;       ` 8                                L   p;     p;       8 t         ʾ              ɾ        Ծ                       L   p;     p;       ( $         <              ׾        ;                               L   p;     p;       @                                               L   p;     p;                 ξ              ݾ                               L   p;     p;        d                                L   p;     p;                               :                               L   p;     p;                                                              L   p;     p;       X                  
                                     L   p;     p;                               Ҿ                               L   p;     p;        H         ¾                                             L   p;     p;                                                              L   p;     p;                 þ                      ;                       L   p;     p;                                                              L   p;     p;                  ܾ        "                      $      ۾                               L   p;     p;        <                                L   p;     p;                                        L   p;     p;       4            4   z     d   p    d      $    x?                  $                    6	                            $                            ;                                                                  L   p;     p;        h                                L   p;     p;       \                                         L   p;     p;                         [                                                             L   p;     p;       |                                                               L   p;     p;       < tD                                L   p;     p;       = D                 !      ^V        +                       L   p;     p;       dD xY         A                      ܍                       L   p;     p;       = D         :        c              5                       L   p;     p;       < D         4        G              1                       L   p;     p;       < x<         )                      -                       L   p;     p;       < 2         z              7        /                       L   p;     p;       1 <                 ]      &        ,                       L   p;     p;       $2 <         =              'U        9                       L   p;     p;       < T         @                      6                       L   p;     p;        = 2         x        e              s                       L   p;     p;       1  2                 7      .                               L   p;     p;        <           Z     	         !   u   3      A               i      g      9       5   e        I           /         '           c   =   %       U             -   O                        _         K        ?                          C   1        +         G     y            [     S        o     ]      w                  #        a       ;              Y     s   )                 {       W                                       k                     q                                  E   m   M      7                            Q                                                       
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ww       5`5                           L   p;     p;        @         g                       L   p;     p;       0                  :      $                       L   p;     p;                 3        <                                     L   p;     p;                 
        >      "                                L   p;     p;       (                  @              &                       L   p;     p;       <          R        `      \        )                       L   p;     p;       H p         N        b      J        0                       L   p;     p;       8 (         ZR        d      5        _                       L   p;     p;       hI          y[        f      ]        '                       L   p;     p;       m t                 h      C        O                       L   p;     p;                 Q        j      T                l                             L   p;     p;                                        L   p;     p;         d                 J      -        o                       L   p;     p;       p                  L                                     L   p;     p;       , l         U        N                                      L   p;     p;       T          k        z      s        e                       L   p;     p;       x          d        |      9        z                       L   p;     p;        8                 ~      q        t        a                       L   p;     p;                 @        !                       L   p;     p;       `           h        V      B        9                       L   p;     p;                         X      >        1                       L   p;     p;       h          .        Z      4        6                       L   p;     p;                 D        [      F        (                       L   p;     p;                 i        \      j        S                       L   p;     p;                 ,        ^      ?        K                       L   p;     p;                 u                                             L   p;     p;        X                                                      L   p;     p;       p 4                       p                               L   p;     p;       H                                                       L   p;     p;       h                                                       L   p;     p;       \ $         *              U                               L   p;     p;        TQ                                                      L   p;     p;                                                              L   p;     p;        x                                                     M                       L   p;     p;       D P         8        "                       L   p;     p;                 Z        n      I                               L   p;     p;       h $         Y        p              c                       L   p;     p;       d <         b        r      E        A                       L   p;     p;                 p        t      `        H                       L   p;     p;                         u              c                       L   p;     p;       4 L                 v      [        w                       L   p;     p;        l         ~        x              k                       L   p;     p;        d                                                      L   p;     p;                                                              L   p;     p;        p                       (I                               L   p;     p;         $                                             =   ?   }                       L   p;     p;       ,          r                                     L   p;     p;                                       v                       L   p;     p;                                       n                       L   p;     p;        `         l                                             L   p;     p;                                                               L   p;     p;        x                       |        {                       L   p;     p;                                                              L   p;     p;       T          y                                             L   p;     p;                 S                      ~                       L   p;     p;       N                                                       L   p;     p;       @ L                                                      L   p;     p;                                                              L   p;     p;       @                  A                             L   p;     p;       h?          ش                               L   p;     p;                 h  
                                            L   p;     p;        0                                L   p;     p;        l                                L   p;     p;        p           (                                                                                                                                                ˸                       L   p;     p;       P                                 L   p;     p;       `                                                       L   p;     p;        x                                                      L   p;     p;        \                                                      L   p;     p;                                                              L   p;     p;                 t              $                               L   p;     p;                 Ѵ                                             L   p;     p;       D                                                       L   p;     p;                                                              L   p;     p;       4                                                       L   p;     p;                   "         H f     0   h     g             h        |     i     0        j                                                        L   p;     p;                                        L   p;     p;       < 8                                L   p;     p;       X ,                       l        )                      
                                ,                                             L   p;     p;       `                                         L   p;     p;       0                                                       L   p;     p;         |                                                       L   p;     p;       \          h                                             L   p;     p;                                                              L   p;     p;                                                              L   p;     p;                 e                                             L   p;     p;                                                               L   p;     p;       H              (˸	         !                    <          i      P              d   e          I   x          /         '               =                            O                                        K                               ,         1     @  +          G   T  y            h  [       S      |  o       ]                                         ;               Y       )                    {       W                        0            D         k     X            l        q                                        E   m                                       Q                                         4            H           
   \               p                                *       .       "       &   8     <       0   2     6         J     N       B   D     X       \   ^     R       T   V   $  j       n   `   8  d       x   z   L  }       p   r   `  v             t                                                                                                                          ?     en(      1 J   <          P ˸P  ;     jd  E       ex  $˸        u                x?   ;               
         A o         x  x?       T? y    6           W   pB         ,  |      ^   @  S     T?    T        DU h      X?   |  *       <    S                 1      ;     X?              TB        T              I       ;             f   0  @?      T %   D        S X      ?   l  t       <    A         LU         -                ?            tU         ?   :     $˸  ?                         ;     @         P        C `          T p      $           0U           @                  TU           U                  A            T                 U              0        @       T P     
   `     p       @                  (          B      $v          q            @              ]           T      *            i   0       S @     1       P        `         ; p                          C                        TA      %                  tB                          8A 0     -       @     Q   P         B `     I       p                 87                        h;                          S      $             0          ?              0     =   @       @B P            `     y   p         T              5            U      	     !            U      <                       xC      (         0         pD @        P     e   `         lD p     P                  <      8	                 U              	            <B                         N 0                    0	            ;               ;              H? 
             A o             x?              `T 6             pB z       x      0A ^             T?        P      DU F             T *       X      S        4      T 1             X?        0      TB m             L<               ;              A f              T %              S              <C t       D      A L       ,      T -       0      ?              tU I             :        D      ?               <              ?              C l             T $             0U >       T      ;              TU H       L      <        t      A O             H@        8      U ;             <        \      T .             2              @ X       L     S (       ,     B ~       X      DB q             @ V             \B ]             T 7     <     A i     4 	    S #      
      ?           ;             ;           C      |     <           TA [            ,D             tB s            D;             8A _            @ Q              B {                             87             ?             h;              B        d     S         H     T 0            ?              U =            @B p       t "    B y        #    T 3        $    T 5       l %    U @       8     W !       (       U K       0        C        D !      xC        p *      $ +       ,      pD         -      A e        .      lD ?        &      (2        p '      <         (               )      U G       L 3      @? 	       H 4      <B c     xB h       2         6      N        < /      \D         0       T +        1      t. M       , 2      2        ( <      B Y       P =      @ S       h >      A E       ( ?      <         7      A a       X 8       9       :               ;      ?    x	       ?               A N   0    C            2          N           \D    P T +   <   t. M                   B Y   @ S   0   A E             A a          <           rʸ?           ?    pA N      C          4                      <            Ћh	ʸ    Ћ          0p      2             "   p          Ќ                   Ќ          p                              pʸ                                       ؙ<                              Ѝ`                                 Ѝp   Ѝ4	Y         Ѝ؎                                 Ѝ   ЍH	Ѝ(      Hy	    _   Ѝ	      Ѝx   Ѝ	   	Ѝ   ЍtE	                  <     r Hr     Ѝ	   ЍX                            <!     Ѝh   Ѝ$	Y         Ѝ   Ѝ	   	ЍؐY  c       	                  <              0	Ѝ@   Ѝ3	                  <      _     Ѝ	Y         Ѝ                            t     ЍY  E      X<9	                  <     '         		                  <     J         L	                  <              P   P	   `	       A b   ?    T    dT 2   A \   B }   B w   B |   pU D   S        LU 4   S &       xD    @ T   |B j   T <    k   T :   @ R   |U C   @T ,   @ Z   U B   A d   A J   A W   T 9   @    B n   B x   @ 8   LB v   @ U   C    (B r   B u   <T '   A g   @U A   T )   $A `   lA P   xB h   B    B    B    4C    C    @C    \C    `C    C    |C    pC    DD    C    C     D    C    @D    C     D    C    hD    D        8D    0D    2    <    p7    <    <    1              X	    Ŀ	                  <     L         PP       H	    	                  <              ȗP      4	   9	                  <              @P          	   $	                  <     |         P<       L	    5	                  <     X         0P       (	   x	                  <     t         P      x%	   ș<+	       Ѝ	   X          L 8  $  P  ,  h X \ x         ؙ             XT	                         `$     x                            $     xP                            $     x                            $     x                                 x          x             (                              (                            `     (                             ,     (H                                 (                            d     (؝                                 ((                                                    , , , , , x, , D, , H, `, , ,     @,     H             A b     <        T      ?        dT 2     B        A \     C        B }     C        B |     B w       S      pU D     B        p7        |T /       2        S &       U "     \C      |C        |B j     @ T     T <       C      C         k     C      T :     pC      @ R       @T ,     |U C       @ Z     4C        A d     U B       C      D        A J           A W       @      T 9      D        B x     B n     C        @ 8     <      LB v     @ U       C      @C      (B r       hD        8D        B u       <T '       1        A g       <        @U A     `C        T )       DD        @D        B        $A `        D        0D        lA P       02      V        p2        2        2      P2      2        X2        2        2        \2      2        2        2        H      2        p(        l        2        x$                                            `        2        P                $                       5       @      x A       B       C      , D       E       F       G      h H       I       J       K       L       M      t N       O       `	  0	   
                     <       \ ]       x    P ˸H    $˸x1	                                   x                                          d              P               <                             (                 ˸             /	     (          ,                 @  <         ȃ T          Xh   ˸    |  (    0	                                  <         [           XЦ   ˸                 |0	                                0  <         ^ D          ЦHX   ˸          l      4/	                                  <         x_           H   ˸             (2	                                   <         l\ 4          8H   ˸    \   \      \0	   p  `             Y                                   `                            <           Tq           0	         $  	            8             L  2        @`            6   t                       @                                                                                     (            <                P         @    d               x  `                @            $     `                                                                             ,       @            T              h         >    |                                                                                                    $                   0  :           D                 X          <     l  =                                            <          >           H    ʸ                ˸           #              (               P      X    0          @                 P           (         p x   `      L          \ <                                              p	        L	Y              0     <	   @             P         <  `     x ( p      8      H      h                                                                       +	                          <  0     P $e @      P      `      (p      p                                                     E	Y                  k	                          <        ,        0      @      @P            `            p                             n	                         <       @ l       а                                                       n	   0     n	   @             P         <  `      T p     X             (X                                                           P ˸              n	         |n	   0             @         <  P      } `     бHp             H                                                           P ˸                 pn	        dn	                 0         <         8 Q   B   "                                 ; ,  ? `             # x                         ,;                                                                                                                                    4   G(    d   O0   ? d      $     $                  $                    6	                            $                            x                            ?                       u   $     $ T   T   d;          G                                g                 h                     e                                                        
                           |                     /                 _  
                       b                                                                                                           j                    `                 	V                 
T  
                                                         ̦  
                       ؀                 ¼                     S  
                       %}                                         S                  a              X                  w  
                        S                     Q                     S                                  i  
                                                Q                    
                                                                                                                            9l                  Yf      X P   %                    t               "                     4                                         ?                                     ʸt            (                       2   ^I                 6   >                 )                                         G                                            L                     x                  z                    {                 E                       ,                     t        h           h                                     t        t        5                 ;                                    7     X    <     @Y | , 9 8  @ 7 7 H 7 7  0 8 l   4J 4i ԉ 1 @? XA % Z O Ȝ dm m Xm @m U 	 hm <u u O D@ Pm ` HZ `m 6 Z  <   l + < u 1 l 0 0 Tm  Pu 4 C  1  4m ܮ 8( +  $C  p? | Du pO \Z t? 8 + ,(                      p  8                     t                 09r                 0  p                 c  
                       Dr s              Q                 _Y  
                       n                                                           
                           i                 f                 j                 Q                                  W                    `R                    h                    S  
                        (             0                                       O $X          |                                                                        (                                                              0                                                                             #  R                     M                     P  (              ?                                    ` l      d $                                                                   W  
               <     S                     ^                                        (                                   |e                      D!                                         7                          ^                                                                         o                  K                     \                  a                 B                     S                       (                                 P td B                  B H                                         ` D         PB <         <r                      
                 +_                 w                     _                     F_                                                      ]R  
                           }                                                                                               E                                                                          Z                 \                 K                     S                 V                  Z                 [                 )  
                        i                                     (                         |                                                                                                                  PH                                                                      JH	       .          /          0          1      M        3         hJ          hJJ    8   	      KhJ    ;   
       <          =          >          ?          @          A                     C         (K    E          F              KD6    I          J          K      +   !          M      ,   #      -   $          P          Q          R          S          T                  L          N          O      /   ث   0         1   8L M2   ˸                         4   8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                                                                                                                                 8                    
                   B     Q                    |  "      0                      <               *           @W+   3       .   %    :                                                      ߢ  
                                           H                  $u                                      0                        (                                          p     <  0(     ) d Z          i          O                                    *}                 ؑ                                      ek                 z        j                L              H                l             V    
            ;o    :                   p             |   *q             $   
            \   ;o    u                v                  w               Px               y             L   8:                   5:                 	|             B   }               ~             r                            Z  p>                                 <                   !H                             x                  2                H   H                          l   -H                                             L  :                     :                             "               n  n                          ^               <             >   H                                              H                               H                (                <                H               B   H                                                  9                   A3                                H                  ZH             f               X             f   H                                                 |  `             x                p   :                ]  :                             B                0  :                    :             
             `L   H                             t                  H                             6  H                                  @>                                 B               N                                               
                                                                         \                                 K>                                 f>               (  H                ,                 t                l             6                     &             b                "MH                             @                N                T   H                @                                            \  )"             xl  >                +"             V   ,"             X   -"                9                   9                	0"             >             	   	   2"             @3"               4"               7"               f8"             F   >                    :"                ;"                >                   ="             bp  >"             *  ?"               @"             `{>                    B"             RC"               D"             6  E"             
   vJ"               m>                    L"             N  M"             pN"             L   O"               P"                Q"                ^R"                  Z1             R[1               |>                    ]1             ^1               {a1                G                c1               B   d1             e1               j1               >                    l1             b   o1             8  p1             X  q1             r1             J   
   s1                >             b   *             F   *             ^   r*             f<*               *               *             B   G                   *             f   *                4   *             r  *               *                *             G                n*             \   *             R     *               :                Q  9                @ 	*             hV   G                ^*             n  H                *             (*                *                G                &*               *             Z   `G                b*             d  G                *             h  *                *                                               x              <   0                   ×              G                b:              pG                fy              T   G                              <  >                                  <      c= (                 P   T d         l   p |      T                     /             6/               j/               /             n   |  /             6  /             /             X      H                /             Ff   /             nn/             D>                /               /             /             /             "/             D4/               /             >:  >                /                /             N  <9                9                   /             z      0             B  qG                9                   >             tG             x   3             >                    3               3                9                    ɐ  (                                                                                                                                            @m m  (                                         D     Z ( |.     86 H  G         Dm <         *  G                     t                                                +k                   
                          g                                                        ;                                         O                 l                                                                     d                     b                  g                 J                 S                     P                     _                                                                                             T                 `                  F                                                       E                     |                       ߏ                                   `                                      Ĕ                   
                  ;o    #                                                           fk                  5                     a                  ُ                     g                                  K  
                        X  (                                         4                                                                                                         Wk                     H                                       Ѣ                 P  (                                 (P     Hm O      Z     pm P(     Z @i                             | G         6 xZ Z $m                         >v  
               pf      ֏                                    |                     b                                         (             \                 7                             5 p                                                         u                 "                                  T                 Y                  \                     :  
               O `Z LG                                       @  (                                                                                      Z                                                             E  (                                 <Z h O                      h2                                                          [               (             hu                 Z                             ȉ                                                          LG t             ck                                   K                  ޏ                 a  (             0                  (Z      hu      |     ,J O                                         <m ]         I P Љ O    "v  
                   @g  Pg                    l                                       ӑ                                   O                     *v                  ڊ                     uk                                  `                  ڏ                                          j  (                                  $5 ) '     m (m     m L)                                         u (         ,u d d? i    M  (                                                                                       h6                                                        O  (                                 0m `I                     ( pI                                         LZ i         XZ 0              (                                            Z                                                                                                    e                  a                                                       !                    Z  (             f                O '  6          Pi      '                                         ԭ O         m h? L6 di    Xk  (                                 @6                                                                                                                 T  (                                 G                              u \                                                                            Fk  (                                                 8                                                                                                                  Б                  A  (                                                         (                                                                                 \G     W                 S                                                       R                                   ӏ                 Hk  (             X?                                      m 1 @Z     X? Li X(                                                                     v                     >                 @                 Y                                      }                     E                                            (                                                     D (      N x? O         . 5                                                                            (                                                     (                                                                                             ߉                 ۇ  (                                                         *                                                                                         b  (                                                         m                                                                             1 `5     G                     Ê                     r                                        (                                                     0                 `Z |'                                                                     G                 X                 ב                 Tk                     Ok  (                                                     O  `G     @G h L?         Hi  Z                                                     =  (                                                             P                                                                                     <  (                                                               u                                                                                 [k  (                                                     P \5          S du                                                                     U  (                                                                     +                                                                             -v  (                                                                         	                                                                         T  (                                                                             4Z                                                                    k  (                                                                                 D                                                                 k  (                                                                                                         '                                         !                     lk                     k                       (                                                                                     1             <5                                          k  (                                                                                             h+                                                     k  (                                                                                         ,Z     P C                                             Ǌ  (                                                                                                 G                          m                     gk  (                                                                                                 i                                                   (                                                                                                                          |?             6     ܏  (               	                                                                                            G                                     v  (                                                                                                                 4                                 Q  (                                                                                                                                                  ܓ  (                                                                                                                         0                           (                                                                                                                             TZ                     ݏ  (                                                                                                                                 C                 k  (                                                                                                                                     4               (                                                                                                                                       C           (                                                                                                                                             ܲ     Y                                   r                                      8                  d                 p  (                                                                                                                                            (                                                                                                  D                                                                    (             O                                                                                                                                                                                          O  (             4                                                                       O             O                                         ]    (             @b                                                                                                                                      S                    h  (                             0     (                                                                                         A  
                B                                                              (             B                                                   0                                                                     S                 M  
                     pf                       %                     բ                 |                  d                 ~  .      !   #   $                                                             +   "   ,   -   %   &   '   (   )    ʸ       h0̎        ? $            $             g                  S                                     H                 &]                  J                                       <                                      ~                  V                                                            ~  
               7     c                                   1                                      I                  $V                 X                                   S                     p                     ʑ                                   l                                                            q                     Ȧ                  @                    P  (                                4 \8 ,     T      p |                                         h- h         U DX B    	`                    P                                    
                     (                                T DO x D     B U     4 @                                         B 7           @    	  (              	                     7 XO     7 B      DY     7                                 @ |         h Y t   p              L  
                p ![                 P                 T                    (                  H                             Y   B     B  m                                                              [|  
               L  	^Y                                   O_                 S                G                 a_                 F  
                           X                  I  
                           R                  t                     @                 X                 lT                  x                     V                   (             (.                           X     :        X           ( B         tI                                      	U                 f                     E  
                 ( 	(V                  n                    d                  i                                  <  P  P   `        _i                          $     $ P  P   Ȣ         o  
                      n                  h                     d                  h                    h                     n  
               |     h                 b                     h                  i                    n                     h                     4K                     b                  n                 -i                     n                     >i                    n                     h                 h                 a                     w                    n                  	i                 n                     i                 Cd                     h                                       Ni                  n                 i                     a                 h  
                        a                     h                     ri                    n                     h              h                    n                  ra                     a                     +i                     n                     ~n                     un                     h                 h                     h                     h                    h                 ~[                     h                     h                 h                 ii                     h                     n                     n                     {n                     n                     bn                  n                     n  
                        h                     n                     n                 i                     h                     h                    cn                 &i                     5_                 a                     n                  yn                     a                 h                  Gn               Qn                     h                 n               n                 pn  
                     }n                    i                     h                     wn                     h                    h                     h                 h                 n                     sn                     ih                  h                    Rn                  lp                 fn                 b                     gn                  n                     n                     Wn                     n                  Dd                  |p                     n                    Vi                     `n                 n                     n  
                    a                  h                     h                 n                 an                 ]n                 h                  pm                 xn                     n                     zn                    n                 K                    n                    n                     n                     dn                                       n                  n                 Dp                 n                 n                 P n                 in                  n                 ~p                  fm                 mp                 h [p                     p                 ̢ xp                 Xn                     jp                  pp               Xm                  ;p                  n                 vp                     nn              Tn  
               L 0     h                 a              n                  n              n                     n                     p                     n                 n                     _n                  vn                     n                 bp                 a                     Rp                     h                    n                     p                 ?p                     \n                    V                     jn                     op                  Wp                     p                     n                 a                 ip                  o                 p                  rp                  Tp                  <p                 t n                  Lp                  'p                 x mn                 к p                 ` ^p                  ln                 < 4p                  o                  `p                  6p                  p                  n                 X p                  n                 p \p                  a                  wp                 ` on                 h Mp                 D up                 hO !p                  tp  
               $ @     }p                 qp                     n                  Vp                 n              p                     gp                     :                     p                    n                     Pp                  p                     [                     h                     Qp                     S                     Xp                     hp                     yp                     n                     b                     $p                     q                     Cp                     @p                     p                     ap                     Yn                     p                     p                     rn                     	p                     Pn                     Ip                     h               0p                 o                 `< p                     o               1p                  np               5t                 b                 t o               p                 Gt               dp              | p                     o                  p                 p                    o                     =p                  o                 l t                    o                  o                 @ p                  &t              t o                     >t                     t                    Np                     :p                     o                     [n                     Yp                     hn                     Hp                     o                     o                  >p                  +p                 h                  p                     7p                 5p                 a                  n                 n                     o                     o                 n                     o                     o                  3p                 p                     o                     Sp                     n                  ]p                     o                     b                     À                 p                 %p                  o                  o                  "p                  cp                 Ap                 p                                      =t                     p                  -p                  n                     o                     o                 h                 p                  o                  h  T  D        ܹ   D ܿ ,       L         \        L    4 l D ( xX        H 8  t        Ⱥ   x Ժ    H , t ĺ p L    X l    \      $    P    `  , D   ̢ @   |     T            <  8   L | `      t L |   0/ < H        h  غ d    \      X         ع ` X \ H |     T  L  ,   p    \ x   0  L          H     l P    `       X ̺ h $      ( D hO `    l      t  d   \ ȹ $ @ $  8  P   0   ( x      h ܺ T  p p   4    8  ؿ l d    ȿ 8     ` d h к t  x |    Թ $ @  ȅ   m  Ԣ   ȥ   4 $  h `<  P  `   , X h h      0 l d    8 @ D  P  п    X 0 , ̹      &p  T                                                         !      "      #      $      %      &      '      (      )   
   *   	   +   ,   -      .      /   	   0      1      2      3      4      5      6      7      8      9   :   ;      <      =      >      ?      @      A      B      C      D      E      F      G   H   I      J      K      L      M   
   N      O      N   
   M      L      K      J      I   H   G      F      E      D      C      B      A      @      ?      >      =      <      ;   :   9      8      7      6      5      4      3      2      1      0   	   /      .      -   ,   +   	   *   
   )      (      '      &      %      $      #      "      !                                                                                      !   "   #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   4   5   6   7   8   9   :   ;   <   =   >   ?   @   A   B   C   D   E   F   G   H   I   J   K   L   M   N   O   N   M   L   K   J   I   H   G   F   E   D   C   B   A   @   ?   >   =   <   ;   :   9   8   7   6   5   4   3   2   1   0   /   .   -   ,   +   *   )   (   '   &   %   $   #   "   !                               R   P   T   Q   T   P   R   P   Q   S   R   S   T   P   T   R       o       p                 p                     t                  C2                      '                                        {                                  ZY                                                                                K                   
                     k                    a                     eY                     V                       
                        Y                    cY                 	T                 Q                 [                                      ?_                 d                                                     ʸw  (             ̉                       (     L         X            }               O         $     X         G                                        s                 L                  V                                        (               }                                                                                                                             R  N  (             0      @O 4             L       9     xO \ x         d `         e     $P         D     l         a  L  (             (P     O                   t     (   c     xe 4 l         Q          X     <}         @     P         a  S                 Ǽ  
                                     8                                 S                  T                  f  
            O     R                                          Z                                  
                   x                   Ӣ  
                                                                                            BX  
                j     L                     S                  \                     ʼ                     S                  e                  q                     u                                       O                 ô                  Ð                                      ̏                  9                     '                  y  
               86 DZ     ͏                                          Ց                  ŏ                  5                                                               J                  J                 (                       (             7     d O W             p     LO X ,     l 2 e     X   O                        O        c                     V                     ?                 Q                                                        V  (                                                                                                                                                  k                  G                 h  
                (                                               K                  B  
                   0(  j                     a  (             `     @  p             (       P TO     H  <     ,                      |X            2}                 'T                     g                 D                                                                         
               C  C                 Ώ                                                                         P                  o                                       [                     d                 o                                       ˏ                                                                        R  (             $     L  O             |     <    C        L h       0                   L     ) $ 3V                     `_                 p                 P                                       E                                      V                 M  (                                        he       O       0i     (G  *              L     a     ,? d  |                 u  (             T}      @* Z             j     h D HX       L         0? h *          l         %          |* 
 Q                  1  
               h Z                          =                     FR                  2  (                     ,l                                                                                                                             =                 B                      k  
                    M D  (             HX      X X             %     % i P      H F         @          ?     (              Ȗ           F                     A                                     r                                                    s                                   z                                      ȏ                  F  (                         _                                                                                                                                              R                                                                        O                     Y  (                                                                                                          7 D}                                   (                                  >                                                                                                         \ 	  (                                               ( () (     DZ (1 *         I (                                                                      \                  I                  Z                                       ȑ                     0                  \                 Џ  (             x|      '                      m ԕ X     }  @A         * Z         8?              )      ?          R                 K                                      &                                      L                                                           Y                                      V  (             !     I                     Z     m       d*  4?         TG          ,m m                  )          O                 x                  Ѭ                                  o  
                                                6                 I        t                  $                           u                   $                            .                                  	                       $  
                         
                   a        4        N                                       C                                      Zp  "      0                      <              @ c   T       @W      T      O# t2                                     "  f                        )   -   /   1   3   5   7   =   A   C   G   I   K   M   O   R   S   T   U   V   W   X   Y   Z   [   \   ]   ^   _   `   a   b   c   d   e   f   g   h   i   j   k   l   m   n   o   p   q   r   s   t   u   v   w   x   y   z   {   |   }   ~                               	   
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   d              P                              3     c                                  `       <          c     [    L#i                    5Y     1 x  G    /i  
   Print(D208); sition(M208);  L                     P            ʸs                                   Q         $ i                     _m     ?          \           h   f        d           h   @f        M  
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                   h                                  L   &     &       p1 1         z                               L   &     &       1                  1   h                   [           h   g                       k           h   R                        Q   h   K                       L   &     &       <          {        &           h                   T                               L   &     &       1 '         i                       L   &     &       ԃ          t        [     ̍        Hh     % "                       N  
                       a            D 3                        $     c        P     d     0   1     e                   x                               ;                                         R  M                            h   4   @           XP     W     4 &    h      S  
                                                                  U                          H)                               ˸      T                                                                        Ģ  
      ,                 L                                 V  ,                                                                                                                            O & `1 1     T1                                       L         & tX                     *  
                         X              ж                                                             <                                 e              h           h               1                                                     {                                           yI                     P    3     t     %         K                     P         Yh     /         \f                                         (           c                                  <         p                 ]           h           #   h                             $     $       | `S         _     D7 ȉ L7        .         $          h       o                  p        &     m        \7     q        &     r                        $     s        8                         L   &     &       t          w                       L   &     &       8          ^                       L   &     &       | r         a           h           o                       L   &     &       H Lr                 #   h           r                       L   &     &       #          Z           h                                  L   &     &       h1 
         g           h           *T                       L   &     &        @         T                       L   &     &       , P         v        =   h                              h           ~                       L   &     &       @  @         i        	   h           $                               L   &     &       V (@         pK        rR           h           V        a                       L   &     &       H @@         	                       L   &     &       l 1                    h   b                   h                          L   &     &       1 &                                L   &     &        @         S                       L   &     &        H         n        	   h                                  L   &     &        h                    h   e                               L   &     &       L@                     h   j        `                       L   &     &       S 1                    h                      h   Ԣ                V                       L   &     &       ,@ 0@         T        K   h   g        ^T                       L   &     &       R          L           h   *L        T        %   h   K      R                       L   &     &       1 S                    h                          L   &     &       & 1         c                               L   &     &       8                     h                                  L   &     &       t@ \@                 _   h                                  L   &     &       & HS                 1   h   ZT        z                       L   &     &       L hQ                    h   XT                               L   &     &       S `Q         T           h                                  L   &     &       pR <S                 -   h                                  L   &     &        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                       L   &     &       |                  /   h                                  L   &     &       l D<         T        G   h   'n                               L   &     &       P                     h                                  L   &     &        < 0S                    h                                  L   &     &       @< \<         <           h   3K        `                       L   &     &        ,         ]K        E   h   T        uK                       L   &     &       t-  R         LK        3   h   K        D_                       L   &     &       0- .         K        g   h   `        T            h       _                       L   &     &       p< |&                 e   h                          L   &     &       > -         S           h   "        0_                       L   &     &       tO <                 ?   h   T        -_                       L   &     &       < R                    h                                  L   &     &       (? ?         T           h   K        HK                       L   &     &       LP .         Y        Y   h   OK        
n                       L   &     &       ,f <-         dt           h   ~K        m                       L   &     &        -         CK        S   h   QK        T                       L   &     &       - D-         d  4   (   D4 d   `0   , d      $    `P                  $                    6	                            $                                                        T                       d                       L   &     &       @          Xd                       L   &     &       x          V  
          c           fK                       L   &     &       P -         U                     P    `     xc     W         `           h   S                       L   &     &       D. p         aK        T                       L   &     &       |P -         K                       L   &     &       P -         )|                       L   &     &       I          ?T           h   b        4   h   MK        K                       L   &     &        4-                 FK        "   h           ,n                       L   &     &        X -         /V        K            h   9_        XK                       L   &     &       | P.         ɀ                       L   &     &       tP L-         ^           h   a                               L   &     &       {          RK           h           NK                       L   &     &       H- `         sl        
   h   b        `K                       L   &     &       ̱          I           h            T                       L   &     &       4&          "V           h           V                       L   &     &       X ?         `           h   (T        K                       L   &     &        P                    h   S        gX                       L   &     &       & <O         T           h   uT        T                       L   &     &       P Q         }d        i           h   d        Ff        d                       L   &     &       ă x.         T        '   h   `        wK                       L   &     &       P          WK        (   h   V           h   AK        K        #T                       L   &     &       >          o        %   h   T        b                       L   &     &       1 P         T           h           T                       L   &     &       P <         9K           h   S        !n                       L   &     &       , O                 U   h   TK        U                       L   &     &       t P-         S           h   S        T                       L   &     &       O pO         ZK           h   8K        V                       L   &     &       h- ,         YK        	      +   !      3      A   Y         )   i         G   9      v  5   z     W   I   |        /        '            #   %     k   U        C     -   ;     K      x    ,   =   y  _   O           ~  ?     E   m       7     }      1                Q   u          w    S       o     ]   {          [     M          
                                                (   *     .         "   $   &   8   :   <   >   0   2   4   6   H     J   L   N   @   B   D   F   X   Z   \   ^   P   R     T   V   h   j   l   n         `            (=        .   d       `@ ,   h@ 	       P        X@ 
     P<     0                ,    1   l@          > -           X1        @        @ /   H7      TQ eK    $˸    -                  <            X P           d                  x                 @         dO        h@                   <P                             0     @              D@               ,         p    @  P@     2   D T                 h         H    |  1               +                   PP   p                    
                0      1     O   ,                 #           0       D             X          H7    l  R         x@   C                *       h@ 	     1               1                                                          x1     4          $   H          8S %   \  @         @ p          '   K                                 -             P                    L                  l@     $          8          X1    L          `@ `          t                                           1       $@         H                           1 !               &           )       (  ,       PS /   <  TQ          P            (=d              d x                                X@                                ,                 dS                                 @         ,            @          x@    T             < h             |                                                                    dO                                 <         8@           %   0          @    D             D@ X              l                   L                                                                     l@ S     ˸   |1 D             |                 @      .   P          < `              p      >            P                     +             >                                  @                     0                          0     8   @         P     1    `         p         R                               h@                                                  7                                    0         @             P         `         @ p                  '           X<                                                                                                0             @         P         `             p                     P@      B                          &      1 !        "               <      H          3                Q        :   0     ;       @         (< P      ?   `     B       p         0<      | F        G                                                                                                  0         @             P         `         p                                                                                                                Q                 P 0      2          6       ~d                     P         h              t                                          @         st                                  <        |          M        k              t                                  <         |         qm                                  <        p          t     (      %d        #h     ĵ D    w        h                                  (                  }t                                                   ut                                  <                  x                                  <                  (x     ,     t     p     df        t        `        &   h   K                `        /K                       L   &     &       - ؃         `        $   h   K        d                       L   &     &       L .                 IY                       L   &     &       P 0X         S                       L   &     &       Ј  .         K                       L   &     &       e X         NT                       L   &     &       p. |         P        A   h   d        yd                       L   &     &       B          DK        B   h   `        T                       L   &     &       - D         jK        D   h   K        lK                       L   &     &       - L.         vK        F   h   od        `        H   h   k                d        P   h   `d        L                       L   &     &                 K        R   h   ed        1d        T   h         nK        6   h   `        `        8   h   Od        `        $T        c                       L   &     &       \- P         V        *   h   a        ec                       L   &     &       PX p         d        ,   h   eR        `                       L   &     &        I         c        .   h   T        `                       L   &     &        \P         _I        0   h   qK        2T                       L   &     &       |% -         b        2   h   K        mK                       L   &     &        l.         h  B                                    & ,   0             #                          ,                                         T                                                                                         {K        `                       L   &     &       - t         d                       L   &     &       X <         K        :   h   IK                       L   &     &       .          vT        <   h   d        `                       L   &     &       Q          y        >   h   T        d                       L   &     &       H 0P         K        @   h   yK        gK                       L   &     &       . -         S        `   h   `        K                       L   &     &       \O @         S        b   h   jd        `                       L   &     &       O          S        d   h   0d        [                       L   &     &       PO          sd        f   h   b        d                       L   &     &       ̑ t         rd                       L   &     &       @ .         i        '   h   h                       L        "T           h   4 1   _K                       L   &     &       -          K                       L   &     &                 d        J   h   `        zd                       L   &     &       Ȓ          d        L   h   Wc        |K                       L   &     &       ` \         >K        N   h   dd        5T                       L   &     &       ,          d  "         D 3                        $     c        p     d     0   1     e                           *               d        b           h           c        l     h X     t        vc        K                       L   &     &       <.          d        d                       L   &     &       Đ T         d        V   h   Kd        `                       L   &     &       D ,         ld        X   h   `        vd                       L   &     &        h         d        Z   h   d        a                       L   &     &       X l         Ld        [   h   -V        &M                       L   &     &       0 X         K        \   h   Ud        bK                       L   &     &       X. T         Ad        ^   h   d        d                       L   &     &                 I                       L   &     &       	          Uc  
      ,                 dh                  `                       L   &     &         |         |  "      0                      '             d-           Uu         Y I       ww ww       5`5    6_                       L   &     &        P         M    ,˸` t                      <   <      ȑ     P   &         - d       &     x          |                 `                      '                                                L   5     0          t            ,             @          L      T       4   & h  M           |  h                                                                    B                L   [            \   &                   0    K   0         	   D  +          3   X  A             l  i          G            5   z    W       |       /          '              #           U       C       -   ;     K       x      =       _   O              ~  4        m     H  7       }    \  1           p         Q   u            w    S         o     ]                     M           
                                                (   $              8  $       8   :   L  >       2   4   `  H       J   L   t  @       D   F     Z       ^   P           V   h     l             0                              P         1                              (            <                 P         dO    d              x1 x                              1                        X7    (˸<                +       p                 X@              ,                @  ,     HT         #   h          |            @                          N     x@                 *         1                                          0          D             X          x1    l            <            %            @                                ?K    ,˸-   $             |             ? @             P         `         l@ p               D            X1                .            <                >            P                +            > 0     .   @        P         @ `         p     0                              8            X         I        X           R      )                         h@       2       0     @         pW P             `     7   p     X@                           ,                   #           @                   '            X<                    [   0     < @             P        `      p                                                     x1                   $        8S                             D@ 0             @        P     L `             p                                           l@                   D        X1                    .        <               0     >   @     P P             `     +   p     >                           @                   0                              8                  1              0     R                |                          $     $       L3 t         h        ,              ( 	j                                  (                  k                                                   w            `c        t               }        x                                  <         8         x                                  <         L          h     4     }        t     x      t        !h                                  (        $          g                     P    (Z     -x                x                                         l `         aL        w                                  <         1         wt                                  <        \ P         2x                                  <                  $x               t        w           w        t                                  (                  $Z                                                   'x            Kf        x           S        x        I                |        of  L           X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X                                                                         X < ah     ˸ h  I                 d                                                        P              x              <                                              &                  4XL  (˸    `7    ,             @             H5T          x57h  ˸          |  5    G                     5    * 	2            5                            5    * 	˸          ` $           660   ˸           D  $             X  6          l         $              78         67                                        3       H5    ?               7  p, 	       Ha    0              4  )    R   H           $ \         `7?p   ˸             $              7             7    8:                                            7      H L   X8          $         88p98  ˸          L  X8    G   `                 t                  x         X8                            8    ܲ                                         $                 (  p9    p9 	<         79P               d  p9    * 	˸x                   9    Y            9  R    9x:  ˸    :tY               x:    ˸            $              x:7,             @             7T             h  t        o   |  x:    E2          , $   )                  ;    l         :H;                                        T        ;    E˸0              D       RP    X             $ l  R                           3   *          0                   R     2                       S   Tf           ԟ  04     ,| ܒ  \  ̟ T h 1  p& 4 \  ؟            ,,  H | < X&  $% hW   @  5   l 0Y   | 8     5     d  & , 1   , H5  8|  Z 5 &  4 ( ؋ 0         $     `   5 $ Ă    L% ȟ   ( @ 1  Ą d      1     1 H     4 2 Դ   8 D  pd  ش    P p X  h   `  , , h  @[ t] P 5  3  1 dP x   1 L \5   `5  4 ܴ   D  8 W                 8f  .   Xa @h d \  [ 2 8&  3 2 \3 %  2 H P  2 8e  $ \  , 0 \t  |  | L5 d 8 d t     |  4 < ˸s                                                           Z                                              2     N                                     .Y                                              s p2 $\         [                     P V  
                !      Wf             Q  j                @1 	˸           !          "   	       #   
       $          %          &          '                    )          *              @         AxB                                                                           xB              (         Aʸ       !   @B             i                     =T  
                       I                  VX                                                 %         s                  h HX  NY                      3                                                                     Z                     cI  
               93 	]V                 L                     K  
                P     \                  X                     3d        im        M      s          $             t                                  (                  t                                          |         h                                          I         X                x        *x     0       v                t                                  <         p         t                                  <        $          t        t       L h h        t                                  (         <         t                     P         }                t                                  <        s 0         p           t     t       t        h                t                                  <        b T         %x                                  <         \         zt      8     gh        o                                  (                  |                       `           sc                     P         }                x           ̍         0x                                                   }               ?h                                  <        ̾ L         \     2      ]c                     P    X     l                x        |  4   @(    d   X   T d      $    (                  $                    6	                            $                            P                            y                                         x L         |        |     l     `  @      8- l   u  d         - m   v  p        P n     X@ 
       8. p   w  0        P h   x  ,        `- i   y  dS #       $ j   z          4? k   {  @         u   |  H7        $e v   }  x@        O w   ~  < *       4. x     1        a q      1       xP r              s             . t     dO         ~     x1              < $       \      8S %       `      @        8Q y     D@        , z           8@ 4     L -        |     P               ? I       $-                    l@        0      |1 D       P      X1        -      `@ .       H.      < 5             P< >       \.      P              xQ +       -      > @       P              -      @        TP      TQ 0       -      - e       |-      Q 8       ؑ      X P              X       -      R (             D        3      h@ 	       $.        <P c               pW ]       ܃        0 7       &                                                                t.      @      T      D '     l      X< A     8      PP [                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               1                < N                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             ? Q       $@        P V        2       DS 6       P@        ,P ^       B        | F       (< =       PS /        :       & &       1 !      "      K       l- T        <       0 )       @P L       1 R      \       H< C     < ,       H      0 Z     | G     \ B        3       > J       c W       Q 9       S H       p- M        O       ? ;        ?       P U       1         P Y       T S       0< E       8X _        - `       ( a       ܷ b       l d       } f       O g       lX o        {       - }               4        ȑ        -                        `        |                                                                                                                                                |f        hh                                  (                  |                                  `        l         c              [               "W     V     L        c                                  `       D& @         ]f                                  <         d         J                                  <                  |     + t    Rh        |                                  (         H         ȼ                         g     Kh                                  `       4 t         c               a        [h        O                |     X               M                                  <        \ 4         }                                  <         %         tI        c      84  ˸t        c                                  (        ̎ 4         p                         [     \                                  `       $h          	Z              c        0]        |V                \     \               w                                  <        Ll (         |                                  <        \ 43         )V       @gn        fh                                  (        X          3m                                  `       \ |3         ,W     8         Z               V        L     d     c        jV     ^       i                        W                                  <        <i          |                                  <                  |        #x     @ \ ˸Y        Y                                  (         g         v              ?     d  
                       8d     Ч hs M  \  
                        k|                         0s     wW                mc             \                                  <        Y          ~V                                  <        s g         Y        1Z     Y (s ˸uM        V                                  (        h 5         \     1 d                    P  
                       \                                  `        ]         >n            L        $W               f_        UR        }m  
                                                         <        4          GZ                                  <        Y           [     i     Gh        P                                  (        l          [                                  `       s           X                            <  Q     `                         w      h @ h                                b                                  `       r (b         X                                  <         .         
Z                                  <        G \         4W        w     (h $b     x         W                                  (         D         L                                  `        g         \        QX                Nf        w     f               δ                              c     H f                                         <        \ }         ?Y                                  <        s TI         \     b     B_     d      
]        \                                  (        } (t         Y                                  `       [ r         V     |         ]               w        c     h     h                         4     Y                w                                  <        h [         Z                                  <        3 s         \        FW     h  $˸c        ~                                  (        ] @         X                                  `       P} TZ         i        L               X        Y                       _f                         C     T_             p                                  <        Da 8         :|                                  <         d         ;Y        \        ˸\        h                                  (        s `s         b                                  `        t         i              YT           a        n          i                              V                S                                  <        t          \                                  <         [         V        V     s N  ˸O        P                                  (        tZ >         ]                                  `       d t\         u        \               W                               b                         Ls     =Y      t        !Z                                  <        3 0b         J                                  <        g          v        b     @( h  ˸                                          (                  W                                  `       `          i     \         i           f                   ]                         <\     W                Z                                  <        dQ D         f                                  <         H         a        9Z      |h ˸L        \                                  (        h 3         k                                  `       g          \                                  <        Y ts         p        !W                         $     Mk                O                                  <        s 0\                                           <                  w        Ԧ     P# T? ˸xi        W                                  (        P          [f  $    `  $ x  ( d     p] ,4 P G , D  , ls ll   s ̴ 2 g 4b  0t h\ %     N              l                 6Y                                  <         8         Z                                  <         <         a        +Z     h d ˸eI        	                                  (        h %         Qi                 p                     ,Y        ,   ʸ,   sa                 ya     8            $  @     h     !   )                              9 mf                                  `         0         K                  W              Ax                 d                  C                   \                                  <        d L         dR                                  (        X          Of                         @     AL                         \     :K                                  `       4          Pf        w                Yc        eh     N   0cc        I       K        d                                                  T                                                                                       `                                      S                                                  +     F                   L     a                     i                                                              8                                                   ;                                                                                           [                    m                                                                      hl                    i                     i                                                                          @                 N|                     k                                                                             8             Cn                     b                                                                                         a                                                                                                           x     \W                                  `                 8T                c                                  <        P @         }                              zc                .Z                                  <        3 (         L     F       
x        L     h ؎     Z        c                                  (        03  h         \     <         a                -}        t                                  `       & 2         I              |               f     J     \        c                                  <        3 >                                           <                  |        uc       ˸|        p                                  (        ԍ          W                              a                fV           ls         '      &W        c                              V     (         M      N   0c                                  <         X         2V                                  <        , ps         x     X P ˸If        c                                  (        d $         Q                                  `       Z H         i                               x                              W               x        &d     R     ;n                              |                c                                  <        2 @         oh                                  <        \                  i  (                                                                                                                                                   Y     ^       Q                     V                                  (        t3 4{         /x                                  `       ` H         c                                  `       l <         x        w                }        t     4              |                                  <                  |                                  <        L x         |                                  (                  )x                                  `       x          c                              Eh                              j               x        k     >     t                                  <         H         Wh                                  <        \ ,         }        }     \ t ˸|        |                                  (                  c        L                x        |        c        d     Ѓ \        `                         t%     Cl               |     B     w        s                                  <                  v                                  <         x         t        \     d D ˸|        |                                  (        r          t     @    M                                  `       \2 L         w                              |                                  `                 x        s                                  <         Th         c                                  <                  vf      `     x        ]I                                  (        ؙ          L        W     L   0|       Hʸc        L      Jf        ;d                              L               O        |     H     |                                  <        ` 8         |                                  <         0         }     D    x      p     h        |                                  (        | @         |      .V        m|                 }                x     *      i                  b                 \                     la                 f                                  m                  i              i                 i     6            $ l      z                 \h                    wi                    v              ܥ )d                 /                                   |     `3 H2 ?    a                                                        ;I                 Y                 b                    %a                               Vn                  Dl                                  Vc                 .}                 i                 i                  =d                 \                 s                  $K                    	        b                    Ra                                                         0k                 RT                 i                                  b                                   a                     b                 {                 S                  b                                      J                 1                 <n                    Ñ     N      J   v              z                                      `                 a              a                 a                                                    vm                 m              b                                   7f                 {                 h                     X                  l        XQ $ d                  v                 S                  CY                  m                  a                  H                             gC                    w               *      oi                 |        x        v                    [      ;      X               }     r        b                     |                                  <                  c                         I        d                                      m                                      $                                                                       j                 h Jl                 ,i                                  <        Hn \         Dn                                  (         I         8l                  K                   (                                                                                                                                                                  V                    ]T                  4T                 YX                     K                    \                 Hh r                                         d     (                                     %                                           h                                          S     |                                     @.                                          X                                          l                                           (                                          i                                               C                                                  4r                             e                                                   a                                 Ը     t                                     ph                                          +                                          T/                                          |                                          4/         r                                 /             TN                             @     .                                                                                     4                                     8             (&                             a                                                                                                                             ,Q             p7                             .                                          x                         q                 @X                                          \    )                 s  
                t ʸC                J_                     ^                                                                       -        v                     O  (             
p g @ t (     T         , D hN 0     z Dh ܄ (   X  h ,h  H      :  ܬ  x z              Jx  
                  3 \     h           |8       Z                           $ D                                  <        G $                 v                     b                     ]d                 K              $i                             {                  s                 s                 |              w                                       \L                 e_                   c              ?Z              ]                     X              DI                                  Z                 F                                   Z                  Xf                    Z                 I                 OT                  <Y                                   ,V                  \                  4B         $ Tc        xW              \                 o                 a                                  <        r p         C                  }                         g     |     4         |                                  `       83          P        ]           `|    C                   Y                  L     Ď |                      ff                   KK                  s        a                 ʸL                                  <         |         >V     .      |                        ]                 r                         Ln                  d  $                         |            ` n     0      @I                 |        t                  $        l  l         u                   $                           p        |     ,      &Y                 hc                                  `       p3 ,         L                                  <        3 |         n        ݊                     J                         5  t        K            L          I            ER                                  <         (!                                   v                 	   
          q oar=        Z-Fߊ                                  <         4         "Z              I                 t                  I        . $ J        G                                      z                 mM                 +                 .p                    4x        4   8 3 	ʸѦ                  s                 i                  z                 s                 9n                     Qx                 V     4       0   ʸVT                 :x                    ;                 v                z                                   p                 t              [                     cT                  Hn                 z  
            Ї     v                     p                  #Z                     0v  
                        Un                 LT                 s                                   Y                 )j                 y                 $  |     P                                    ܵ        8s $                              C                    
y                 S                     K                 Y                 7l                     m                 K                  h                    s                  Dh                  y                   M                 GX                    v                     I                 a                  )T                               z                     i                 p                 #a                 +d                 KT              ˸                                  K                                            v              $ $ =                                  w               i     0@ l    $ =                x                 s        t                  $         | 8         u                   $                           FT  
                      m                 p  (                9 g @ t (     T         , D hN 0     z Dh ܄ (   X  h ,h  H      :  ܬ      ҏ              v                 Cx  (             Ъ9 9  9         O               s       P  H X d         <   H        D p ʸv                     t  
                                           o              d     v  
                <                               e $ a                                  <        s          $k        h                                                   (?        \                          W     h t  X s `   g 0h d                      b                 "                  p        % $ k                                  <        8t                  AY  
               *        Pl                 /                      s               ۮ                 |+ ,  
                ;o   
                    t g                 y                 Td                                      FZ                 An              ʸyh                 mh                       da                              .      d  ܸ PQ     |  l7     p          5     p1          b .         da             L          D  ̅ $          ]  %      8              d                          da                                                                  $B                      Ț 0 0 4                 da     N 0Q             ذ P H     pQ      T 1     , Ȇ                T                             da 8 x              t      4     / Ԅ ĉ  [ \  |         <O ,                                                 da 8      L              ؂ |      ,         h     T         ̤ D     s                 1                 oL                                                                                      p                 C                    v                 z                 Y              yc                                    {v                 ~P                                     t              s                 p                 C                              Q                    |                                  'V                                          N                                  C                s                 h                     ݦ                    :n                 =                    4n                  ~v                 v                                                         o                   @_ / : t  D A \      @R \ D .      z                     fT              ^                    "d                 9                    
                       oc  
            t  '   i                  ^f        Z                  |+        P $ s                  w                  9                                               & HQ                            H       X       9                 O                 T L         X d             C                 0  +          9                              X |  X d ( X                  $                 p , |B P             9                                     @   <                     8                       ص l ,                 9                 Ć             * $                ܘ                      < X l
 ,                     9                        e                      N          i                                    l                                  <        `          ^                  ` Ĉ [ g d      `      P   (} t l     <l                 P                                  <        } P                 [c                                  <        d          b        a                                       d                 k                     p              ]              >l                    TT                     Um                   y                                   7n                  ي                 [              b                 a                 ܦ                                      n                                   _                                      6l                 S                 Rx                 5a                 \T                 n              V                    K                 z                 q                               t                 v                 h                 Kx                 O                     C                    9              
              Sn                     XI                 o                 Nx                  t                  h                 t                 ˦              `                     ڦ                 p                                     Ux                 ( 3i                 h                 wm                                  <                  Y                  l         $    L   L                 C                   i                  Fl                    t                  P                     _  $                               	   
                                        jY                                                       l`                 5n                 <U                         hX                     Z                    m                 J                  a                 +                                       K                    o                                     C                K                 K                 4/ S                     -d                 \                 v  (                                                                                                                                                <+Q  
                       oa                          Xh $ za                                  <        [ ȹ         `  $                            a                                  v                 jI  
                          Y                 v                  d                                  <                    
                      
     (                                                                                                                                                           8 p =x        t           L  $        4  '      u                   $                                         El        t                  $         @ 7         u                   $                             $                         @ 
                ` F t                                              C     C        Y                   
                                       a                 a                  b  
                       7I                  s                  i                 X                     9 
                      	   K_  $             (             $                                                                                                                                     o                 2 n                 o  
                \R  "                          C     C       lm          k                                   7k                 |s                 N                     Z                 z                 7a                     Z                     ^              x                                      d (                 
l        C                    Fx               Ъ9                                               & HQ                            H       X       9      H?     O         .     T L Ԇ G ( T     X d P $;  C                                   9 9                    X | g   , X         < p He $                           L                     9                        e                      N          i                                     a  (                                                                                                                                                     "  
            "   @;o    ?                    mV                t           t+ x $          D       u                   $                           o               	 x5                                               & HQ                            H       X       x5      H?     O         .     T L Ԇ G ( T     X d P $;  C                                   x5 9                    X | g   , X         < p He $                           L                     x5                        e                      N          i                                    Q  $                ˸m                    h                    C             	   K                    ʹ  (                 P 9  9         O               s       P  H X d         <   H        D p     \                                      Fn                       t           hn         t                 H      C 4    t                     J                         5  t        K            L          I            
 
                      |                      z  
            *,Z                 K     |G         $                       ;o    2                 jc                    J                         5  t        K            K                    z                                      p                 p m              !                 'W                 b                     f                     y                          Pl $ v        v                 a                      `                                                                                         Q      h                      `                                                                                     }                                    `                                                                                               T                          `                                                                              (     dh             hh                     `                                                                         t p     X                                      `                                                                     \      t                                           `                                                                 tQ                                                            `                                                         <Q d+     g                                                      `                                                       C                   p                                             `                                                 ,- (F     .             d                                                 `                                             (D >     \l             Q                                                     `                                           %                                                                        `                                              Ds             h                                                             `                                                                                                                              `                         d         Q             F                                                                         `                      b <y     h             t                                                                             `                 Q      h r                                                                                          `                   0             ̈                                                                                     `                                                                                                                      `     4 `t     P          Њ                                                                                             `  $}     `%             |                                                                                                                     `          |                 Uf    $˸                     8           ȍ d   @                X    `      Q P         P x         (D          S    p      h P   P       <           (   0       D                              H                         0           @             P     PY   `        p     07 	                                  8l                          6 	 ˸               
            ċ         Xش0            @     $    P     p`           p     p                ش                 $         @                 $                                              0             @     tP             `          p     p                         $              H       x6 	˸                 x                  $          $ <  0     p˸@         P     $       `     07 	 ˸p        hW                  Z                             R                                                             Z   0        @     8˸P         `     !       p     Y                 *            i           |                  R        (5 	˸     (                 @             0     $           `|    ˸    $           3           $&     @             P            `              p                  @       !                                             ؋        h0                                                   0     ʸ@      P           `     0p                 $         HP                H`     P                 $         ȉ         ʸ               Y   0         @            P     R   `        l p                 :˸     x                                                     ZlZ                    H;˸                        0     X ȵ @     P            `     $    p           @                p                 $                     x4*                               t 0      @            P     $    `     0p                 $         H              ˸        0Y      $            F                              ˸      0     * 	˸@         P     $       `     `p                           L     ʸ              Y           `                  nT                        0                      ʸ\                     P    А     c     s         Jh                                         d          c                                  <        2 |         c                kc                                          <        < 0        wL                          $     $        X         |                       u   s     s *   *    \         g  
                      `                  X                     WM                                         B                     b  
                   \5     ,j                  h                     P                 j                     sL                                  d              W  
               ,     &                     km              I                  +K                 n                     _                     j                    T                     ch     X Ȏ        a                 n                     n                     V                    `                     L                     b                     a                  ]W                 dM                     n                  b                 h                      a                 K  
                        %K                     n                     2K                    n                 L                                  <        H          b      3     RM                    jL                     `                 n                  _                    U                     _a                 Ef                rm        Mf                qM                 n                  I                  fa                 L                 Km                     Jm                  &j                 Lm                  j                 ea                  n                     Fm                     Im                 vL  
                        n                     V                  I                     b                     Hm                 b                     ?f                  hM                     I                     n                     n                 Am                  Bm                  j                  U                  @m                  Nm                     <m                 , t       t        7m                     kL                  j                 ( Dm  
               1 @     -j                  SI                 Cm                 n                     
j                 }a                     1a                                   }L                    ;m                     ?m                   j                 zL              j                     Qh                   g                  j                   f                  =m                 5 Xc                  b                 | b              , g                  LV                 8m                 }M                 ( d                 1 g                     g                  II                     I  
                   p     9m                     :m                     bd                     M                     L                     5m                     Em                     b                     j                     j                     >m                     Y                     d                     6m                     a                     'j                     Gm                     d                     \c                     Vm                     b           ԟ  04     ,| ܒ  \  ̟ T h 1  p& 4 \  ؟            ,,  H | < X&  $% hW   @  5   l 0Y   | 8     5     d  & , 1   , H5  8|  Z 5 &  4 ( ؋ 0         $     `   5 $ Ă    L% ȟ   ( @ 1  Ą d      1     1 H     4 2 Դ   8 D  pd  ش    P p X  h   `  , , h  @[ t] P 5  3  1 dP x   1 L \5   `5  4 ܴ   D  8 W                 m                     d                 "j                  g                  $j                 i                 `                     d                     Zm                 g                  g                  d                 d                     `                  g                 M                  g                  |                       d                    zM                     b                     g                     g                     g                     d                  RX  .         $          h       o                  p        &     m             q        &     r                        $     s        8  cf        d                    g  
          g                 g                     h              l  c                                         $          p                                  <         `         c                                  <         ̐         4d                                  (        \          c                     P    t     t                                           T         p              0V                                  <        p          h        h                                  <         [         c                                  (                   
h                                                   p                                  <         Ⱦ         t                                  <                  lm                   d              
      	                                                	                                          
                !      "      #      $      %      &      '      &      %      $      #      "      !                
                                          	                                                	      
                                                                            !   "   #   $   %   &   '   &   %   $   #   "   !                                                                   (   )   (   *   (   )   *   (       g_     ,   ʸ1x                                  <        $ H         It               t        t          ,K        v                                  (         ,         V  ,   
               3                   h            $          Ha                                     5  t        #          x                                  <        P |N         i                                  <         h         t          t           t        V                                  (          $         x                                  <        0          Z                                  <        [          V                    e                                   K                                  a                              }              ]                              h                w                                  `       0          -l        .x                                  <        \ $1         x                                  (                  t                                  `       d           BV                                  <        l           |                                  <        X t         L      Y     |        }     @ h  |                W  
                          L                     % 3 . Z                                         P3 .                       \                     D                                                 	   W                     \                 \  
                        W                 W                     \  
                           I              `    & \  <h [                           3      d3        m                     h  
                   ʸLx                 L                   \Z 3 % @\                         % @b     ,Z r         1T  
                43 V                 L                     I                     L                  VW  
                       pDI                   
                           L                     ZI                     L               nI                     Z                 L                  V  
                       5v              h    Z Y <3 s 0                         Dt 2     Y lh         \m        L                  LZ                  \  
                   %     |I                 Z  
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     <    `       .+x        '                  ;T                     Z  
                       (Z                 gI                     ~L  
                           c                  ]                  i              h%     % 3                                               & %                          h           Y                  c        dI  
                   wI                      XZ g P tY s     @s \     1 2 2 %     2 h%      L                      %                                                     h             Ih                          h                                                                 i                             P                                                             L                  s h 2 [ %                         0i k     % s         Ҵ                      3 % g 3                                       T 8\         K                                                                                                       H f     0   Q     g        ̏     h        t     i     0   8Z     j        ̵         sm                       u   s     s *   *    8                 u                                                               :                     ]                                         4                                                 J                    i                 f                     |      P        _c                                              P                                             f                    
                           h                 @n                 '                  a                   
                       i  
                    43                  b                 h                     L                     |d                                              h  0                                     d                                                                                           h                                                          ؚ                                 9Y                                                                                      Hf     D  s kf         a                                                                                                                    Q                                  (                  Q                       
                        _                                               Ћ      | 2                         t        (P        h            9 mm        %                   =f                 b                  @  
                       |    $˸                               <            	 	P   ʸ        d    	       x                                             X 	D   D3              	                                                X 	    Dʸ              	,            @                  T               h   	    ʸ2 |        	X 	                                                 	  D                   	@                                         x 	 	0  ʸ        D   	    R   X                 l          Z               8 	D       Z       x 	                                              8 	    Dʸ              	  R                             4  ԍ             H   	    ʸ@ \  ԍ      	8	 	p                                                 	  D    P              	 	                              P           X	 		 	  ʸ       P $   	    G   8                 L          l2     `          
 	Dt  <     l2       X
 	                                              
 	    Dʸ              	  Z                               D             (  
 	    ʸ <  D      	 	P                 d                 x              
 	  D    |3              x 	                              |3           8 	 	  ʸ       |3    	    F                    ,          D&     @           	DT       D&     h  8 	         |                                      	    Dʸ              	                                \                	    ʸH2   \      	 	0                 D                 X               	l  D    p3              X 	0                              p3            	x 	    ʸ       p3     c        L        CZ                                  <         l2         |                                  <        2           L        L        bf                                  (        g x         }                c                 Z        t                t        ^        ^i                  c                                  `        (B         |                         [     |                |                                  `                 Zd                                  <                  i        t                                  <        T          |                                  <        `          Y                                  (                          gc               qI                 c                                  <        3                  L                     Z                  dc  
                         V                 `        p        w        p  "         H f     0   Q     g        ̏     h        1     i     0   8Z     j        X                 jf                 	   }     h cm        rc                  c                 <  Ҋ                  	t        I                 O                     c                 " 	Y     Ph (    Hg    hI                 @ 	c                  	L            ?   L                     {I                     vV                     L                                  (        D          fc                         0         9 L                    c        |         x      0       vI                    c                     |        ac        L                 x        x        I                   }     X i        W                    Z                    c                    V                    ^h  
          L  
                       L                  t        3  
                       EI                     Lf                	M                    L                  	     | `    `     af  $                  3                   h                                  $          (               h  
      ,                  Y                     L                 V  
               h         L                 c                  L  
                   43 rV                 c                 -Z                    -W  
                       c                 bV                     L  
                 ʸc                 V                     L  
                       \                 K                 V                 L  
                       K                 L                  W                 I                  ja                                  (        P X         V                               }                      p ܰ        c                      t             $        < ,} Ї      u                   $                           |m     0     .      pc                                  <        (          L                                  (                  Nh                     P    <     t     8         i                                                   hm                                  <        D č         V        Vh                                  <                  s                                  (                  om                     P         ~t              c                Gf                L                     L                 c                     }I                     mI                 sI                     c                  L  
                       c                    L                 V  
                           a                     &u                  %Z  
                       	W                 %h                                  (                  c     3   L                 L              zI  
                       \                     V                 L                  S                     \                     Hd  
   4                \                 nf        )                             P 9 Sh      V                 qc        o        W                 W                                                                                              V  6   +(   P d   0    d      $    K4                  $                    6	                            $                            lZ                                    V  "      0                      <              Y           @W   "         M  0G                                     \  
               s |        |              V                      3     3                                              2        L              p!      h3 H\ X L\ s         2     x\ s . d&     2 X] 3 43 L                  2                                                                         .  
                      L                 Y                 2W                                              (3 h      $3 x[                     . 	k                                                                    Y                                        Rf                                  <         p4         x     *    l   =h     H      t        t                                  (                  "h                                                   ^c     L p (   ( T @ |    0 ,   \ h H3         x     t 4      lc                     P    h     h               h        	h     .             t      k               t        t        GR        rt        \         t                  $               |\         u                   $                                   m  .   Xa @h d \  [ 2 8&  3 2 \3 %  2 H P  2 8e  $ \  , 0 \t  |  | L5 d 8 d t     |  4 < t        $h        ]h        oV                                             	   
                  `3 	3 	         pf        ET  "      0                      <              \ *   *       @W+   3   *       M x                                     u  .         +   ,         
                              -            .             !   "   #   $   %   &   '   (   )   *          /         0   1   2      d                                  (        X x         c                                          d         Zh                                  <         4         t                     P    X     t              _h        <f                                  <         T         t                                  (        d          t                                           ؍         Vf                                  <         ȵ         t     "       oI                     P     G                 "          #   /   X             %          &                               ^                  `                  b                  d                  f   	                       i   
       j          k          l          m          n      -   D           p          q          r      .   H          t      +   u          v      ,   w          x          y      0   z      1   {      2   |          }          ~                        !       J          L          o          s             $          '          (          )        "f208 (this will take a while!!)"; Q  
   qEigenform(D208[1],820); um  
            
   ;o    p=                         ʸ \                                             :                                u                 H          e     ˸v         1n                       u                  0         SR     ʸha         c                                u                            I     ˸K         GT     ʸW         K  (             9 9  9         O               s       P  H X d         <   H        D p Sx  (   	               J                         5  t        K            L     6     I            9  u   (/ $ 8  #  P 4F L                       u                 $  /         |      ˸\                 ]                       u                 LI                                 u                 Q ^         yi     ˸Gl         i     ʸP                            u                  s         u     <˸V         Q                       u                  Z              <˸a         Tx                       u                 л H         =     <˸`i         KX                       u                 P          _|     ˸zf         |c      ˸if                 0n                       u                           K         v                       u                 l .         a     <˸x                                u                 $          d     <˸"         h                       u                           VR     ˸#         Ul     ˸~         t     ʸx         y                       u                 |          #                       u                           p     <˸-         W                       u                 x          a     <˸Qf         x                       u                  D         {c     <˸K         d                       u                  .         O     <˸|v         K                       u                 ?                       I         w                       u                 \e $         v     ʸ/n                       u                 XI          `T                       u                 T          d                       u                  t         h     <˸s         \                       u                  t         Gx     <˸         HY                       u                  `{              <˸8n         [                       u                           LR     <˸         Y                       u                 0I X          0     <˸         Tl                       u                 P          |  $   C  ĸ  3 Xt  D F P ,a     X `  d\   \/  Q Q s  e l Hg P  e X     K         GY                       u                 p .         vi     <˸l         V                       u                 إ 0         J  P                  3                               S                      $                          )          -  t        +  t        #          ,  t        4     @P     $  w   Xs l %  t        *  t                  1     $     Ǧ  
                ;o    t  (             |, , d ܡ dW h W      Y I  l X o       Y DB W     1       |W     xg  X1  1      v  (                  ` \ 7             H      X x 0 x: 8 V      t            и              l           U  (                               H   `   d     D p         d         g HG ,     4     NI  (             h <b th d} <         Di     t h Db r   Le       B r ̆      z         1     xh     LX     L  
               B;o    ^  
                ;o    y  (             l t T | $             8     Tb ȸ       - l      % ؐ     @/      d         .          t  ڑ  
               ;o    C                    z  
               ;o    |  
            ;o    I  (             1 l P 
  1  D2     Y  $   l        ] 0  2     F     Љ 4X  0 HI     [  
            ;o    &: 
               *    	   S  (             \   c             P      ,I < N d         E \ x l, c           k       ( (  
                  ;o    v                 y                 X                 2n                     e                  ?l                 zK                                   h                  uI                     6d                  K                                      t                  K                                      .                  ,                 @L                 p  (             С \ 0 <  C     C      O Y  E S B ,D     4 D <1 T  7 D1 % PS          d 6     O l a                     k  (             -    P% `         h7 h2  g        x 2  g  X       I   \I L       (             0 h $            8 `   , <         D  d         T <      S  
            @         a                 P                  7                    Bn                 SY                  b                 ik                 \                     X                  =Z                     ]                 QZ                 Y_                 Z                 X              \                 >Z                 GL                 Z                     V                  k  (             $ $A D ( TD D N  D     ܍ 05 HD e  tD ̭     $3 <A ?   T tA 0D pA     D  `N D A     V  (               t  (5   h  X 1     u Lm    0 <} |        , 4      o     !  8:     x(   
                ;ok  (                 D N  X  G       T} `  8 % l      *   |X   h `U      c L8  i )v              :Y                 U                     U                 C                    }V                  [                                   i                  FV                 (d                 C                    gL                 o              
   C                    wh                 |R                     <V                 VL                 <a              P              
   U                  n                     nm                  Y                 U                 d                 &K              l                 K                   (             XL DL L hL `M L M L     DM M \M L M M L     L M xM L M L L L LL     L L 4M L 8M     l  (             F lE 4F F xE PE 8F 4E     hF E dE t` F lF E      E E D E ` E E E tE     E F   F E               6   u  
            ;o      (                <5   P   0 (l      P ( \ @ ԁ `      ` T 4 d 5 P 0^ D     (  d 5 \!    q                  J                 V   h  (              2 ( L Ԋ ̂ ܂ l4 (&        | , W h     X   0 d $ ċ  5        8  ( 0     `  
            H   
   ;o    w                 w              
   w                 l                 |t              C                w                 w                 Q                  +l                 
   y                 w                 o              v                 C                    w              D                v                  
   l                  Y                 y                 D                 
   w              
      l                  l                    v                     C                 0Y              T  
                  ;o    H                  
            *d  ;o    H                   e  
            b   ;o    JD                    a                
               ;o    C                      
            H   ;o    RD                P  (                     B r     |       87 hr   r      lO  X  H| 7 P  d     @ hG      }    (             i x  D 0  d       P p   d  P        `  |              h                            Y                 C                   p                  C                v                 Tt                 X              
   v                 KR                     X                     k                  Z                 p              z                  ^t                 C                    K                 ct                 w                    S                     z              y              z                 z                 z                  v                   
               ;o    z                               Q                    C                   o                    œ                                   }Q                    C                ok                 C                                  (                 C                                    ē                 C                                  2D                                     C                                    C                                 
   .              C                O              P              &                    "   x                    C                    2v              
   j                 Yt                 C                    Ԕ                    (             pi} } } }  | |} l} }     | { } hp } |  |      } } ~ } V 4} < |     L} } ~ } }     yx  (             p	$ l  d P  <         $  h       v T   0      (        D  h 0-´  
                F   ;o< 	s=                      (                XU ,  0U  |, x U     x- - DU  - ĕ -      $   (  8-        ' U xI   T : 
                       <:                   : 
                       ?}                 Au  (                 $ |      T     %  h   $2        $   | ` P l     2   T        (                o 7 U 0 7 ` | T     | | 8V | 9 X- |     p $E P8 | | `}  8 |     Hp A o o      x              j                    9                 Ak                 J                 S                     C                x                 a                 0              
   k                 k                    C                 Vk                 k                 H                 C                   }                                                                                          0                  F                 C                    =                 ȱ                                  O                                     y  
                  ;o    M (             	[ \[ T[ $[ Tc [ D[ ([     p[ [ [ [ [ X[ [      [ [ [ x[ |[ [ 8[ [ h[     @[ [ [ Z [ O/              ;  (             $  9 8 8 7  8 l9 ܼ 9     9 0 & l ( 8 (9     \9 8 0 8 x9 3 8 P 0     |8 0 9 7 @9    l                 n                               &   Ƭ                 ڍ                 |                               |                 >                                  2                                   V                  C                   Y                 C             
   Y                 C                    Su              D                TI                 C                L                 C                {                 7X                 WR                 x                 xd                 C                    K                 t              su              (   C                    L              hR                 ^u                       (             h_ _  I | _ _ $`      _ _  F  	     _ 2  `' @3 % J       ` _ 2 _ HA     xk                 x  (             @ <  ( | ( @ d       4 2 , 8 | ̿     L  `      X (      * |          CV              *   8 @           5                            "                                 "                    $     ,                  4     4     <     h             x     "          6             L     6     6     d             7          7     6     8          6     `     47             t     (7                       7               HB             $                            $     D     T     `                       |                  P          (                            l                  H                                 l               (                                                p                            p                       8                        h                                                   <                4             0     (            D                   `                        d                            $           ,      <                   D     $     @              0           @                  H      H             L              d      T*                               \                   l      x     <                        p      $                   \     x                              @                                        (!                                          !                                  P!     <                  l                      x     d                                                            X     !     H                             !     !             !                0               $!     x     l             \!          4!                       <!          !                  H!                            t     h!     L!               T                       `     0     !                  x!                            t!          H     l!             8     !     !               !     @     `     p             !     ,          !                  !     !                  D"     h          !             "     !          *                    !     @                  (     !     @"             !     \           !                  "     "                            t      "          h"     X           p"                     4     ("     L                       4"     \             x     "     p     H                  ,"          @           d"               H"             <     X"                                 "     ,             \"     h     |"                       "     H     "               d     x     h             "     T          t             "                                 "     "     `                       " " v                                                
D                   ]                 O              &                       D                i              C                
   k                 5                                8              .   sk                 wc                 3                                                                  4   k                 \                 C                                    D                    I                 k              "   L                  uY                 C                   &               D                    Ɍ              .                 zk              
     
               D  ;o    ÿ  (             h h    ě        < H l        p 8 T ı l 8  |        Л   @|  (             _  \  L t .   {      P  h |              L @ ,        y У  7                 i              .   d  (                X  $N  |  ԓ         $M L       M M  Д  M  M      ؔ M M L  QM  
               ;o      (                $ 8) 8   *       $    , 2 \      0   4   ) L l      ( )    *;: 
                   7:                G:                                 d                 ?                                                        (                                                           R                                $   C                                  D                                                                                       u                      	                 |              C                                 2                    H   C                    Ќ                 C                    ؉                               C                    ;                 C                R              D             	   <               |              A                 C                              6   ]  (                <  P  - T      & w  Ĥ  $        8a H  `w 4t        X |w   H  xn                                    }i              @     (             U|Y p} PY V ,E A A P     D X LE [ X^ ^ >     (E $W ^ X @E ^ ` ^ $     PW 0E \I ^ 4E       (                Lq R Pq q R > q \q     $q U hq 7 q R q     $V R q q xq 8 q q q      q ,U R p   O:                 8 
                   ::                                    I              X   
   x                 V  (                ď  8  0 4  ̗        p  0 ܎     T   ȗ   < h P     Ȅ < 8       0              F  
            R   ;o    ̼                     x                    [                 b|                    `                 C                                     C                   tb                 D                 V                 C                   #              f                    D                   L                 L                 c              	a              `                 y                 jW              <   RR              C             	   m                    nL                 iL              %      3T              :   D                9L              6   `              s              }              C                    "                                        
                R;o                     ?                  D                                                      i|                 5D                U_                 "                 <   C                    V              
   }                                             $      C                                       E                 ,                 <              C                   X              i              H   C                               ,   C                u              Ǒ                               )      X                 C                :                 9                                   ,D                    /                 ,   T                                             D                                  m              
   ;_              &   D                A_              C                                 D   D                   #u              J   -              Y                 k              (   F   C                                                   "                 V     
               ;o    S                 c              2                 P                               *                       &   D                                                     Li  (                T P 8 D 3  3      0 # $ ,3          8P X3   3 x3       @ , U h T       (                 , P R S  P Q P     Q P Q Z P Q HP     Ĭ 0[ Q \R ج  pP Q DP     P P R  Q    b                    ߝ                 z                      (                h H \ d p x   T     ` <          , l | $     t        D                       ]                    D                NX                  ؝                  &   C                    0T                                                           ɡ              L                        	D                                 .   y                     sp              (   =i              &   3D                    Hi              6   d              0   b              0i              ,   1i                     en                 D                 Ri                 `                 D                    Oi              N   Vd                  GK              D                    `              D      .i              b   j                    h                 (i              C                                 ,   Sd              h              
   Wi              h              ,   C                    B                 h              j              ]   _              2   d                 p                 C                    h                  C                    i              D                   Bi                 .   Ed              
   Ti              6   C                              .   C                   K                  i                 i              $   n              L      h              i              0   kn              R   }              F   L  (                 S R R R Q S S S     S R |R S T S R     hR R \S $ TS ~ R R  S     pS S S T 8T      (             @I x f M 8o M hf f     f { 4 DN N <N 4     f f f 3 dM | p5 M (g     e `N f f  <     ߁              n   	|              b   D                 8                                      D              x=                                  0   L              8   q              f   E                 D                   e                 (   |                                   7D                                  b   ^              D   ^R              F   9                                  C                    j              4   |              p   N                                      #D                   u                                 Z                
   V              `   >  (             s w x Xx r O s s     <x w O Ps s s w     s s 0s ,t s s s  s     $x ,x (x w ts  	W  
               ;oL              <   C                    Lc                 AD                    Da                 La                  C                b              2   C                Zc              
   Gc              2      Ya                 Kc              6   C                d              ,   Va              Fc              ,   6I              "   C                   tM                 g              &   U              R   M                 Jc              `                 b              ,   Sa              T   g                 C                    `                 D                	   g                 `                 Nc                 ?c              
   x  (                 8  d l h        , 0    U     H   P  l d X |         h   	k                   (             0 	x3 3 & + V V A 3     3 U U  V 3 @B     V U A A B U tV t3 A     B A  A 3 v                    'v                 u              
   u              v              f   C             u                 D                    E                    u                  u              u                  C                   j              *   B              2   A                 6   C              $   OD                   D              2   E                 u              D                 6   K                 I              h   D                    L              <      Q              (   O              {              @                 N                 B   *D                    C                            t              f    (                Dd c c c c d (d 0d     <d c d 4d d c c     c c c c Ld d c d c      d c c c c    D              B   V              P      
|              *                 t   <              .                    2                            C                                 
   U                  9D                                  
   2   A              :      FD                {              .                 F                 C      C                    #                               4   C             	                                  &   Լ              C                T              .                                  C                                  
      C                                      C                    P              (                 h   b              2   {              f   zC                                                Q              {                 9 (              	0  d  x X p      @ <   8  T     p     D         |   P H 	4             :>  n 
            8           X              <   B              @                 D                               6   α                               6   D                                 H   %D                    0                 "D                                  
   }              
                 @   
   C                	                                        2                 6              2   +D                    1                                             /                 v                 5              .                    D                    4              (   3              
     (             $  t   Ի  p      P    ̼  ,     н  D   d ؼ L      | `    l&   (             (	   $ D  8  4     P ̫              4 t  Ԫ       @ ` < ت  k  (             I	, (  h X l  P     <  L t H         0   `   @         \ T     ~  
            4   \   ;o    {H                $  (                h p 0    \      0   ,  @         L                   >  (             4iTa ` xa ` a ` b a     |a a _ a la (a a     b ` a a a 4a h` a `     `a $b , a a     u                               r                    -D                	   W                                             8                 N   y                 C                    ̱                 C                                  O              H      
              F   ?              Y              ,   m                  
                               >   6T              :   C                    W              i                                             |                 |                 |                 |                                             :                 l                 $   \                                   t     (                   p < $ 8 X Į      ԯ h    d      0 @ |  l `h                              x   K              R                 6                 e   8                                  j   BD                 I              d   G                                                Z      &              N                                      f 
            F  ;o    :                 z                 =D                    o              z   z                                aC                   R              J              P   ID                                   
            @                        
                                                      X                     N                 Ы  
            ^;o    n              pC                o              @   x                            J   o                 w              ^                          f              C                   3                 C                                     ?                    nc                                             h                 :                 V   ^                 C                    h|              t                 >   ,x                 C                    T                                                       m
 (             .  . / x. . $/ . . /     . . . . . . .     p. . / . . . |. / .     . (  / . .                     |              b   L  (             t  H  ,  ,  L        P LD             @    $   `     (       zx  (              D( (6  06 x5 6 6 L(     ' 5 5 <6 \6 ) 5      t6 5  5 ' ( <( (     5 ( 5 P5 p6 DG {  (             d6D\ ,\ P Z D5 [ P] 0     X5 |Z 4 4O [ Z 4     pZ p [ $ PZ Z \ 5 45     `5 [ L] \ ,^     p                 C                   }                                  F   ?                 u                  |  
               ;o    %              N   *              >   6k              .   1k                 !                 1              ^                    i                  C                                 <              j   B              ̖                                  "   C                    Kk              R   !                                                F      /k                  V   $              C              |C                   )k                                   V  (                + <* h* $* |* d* ) T)     * ) * * \* t*  *     ) @* * ,* ) * ) x*      H* * * * )                  ZEG (             E$	6 6 7 6 6 6 $7 6      7 6 6 6 6 6 7     6 6 7 7 6 6 07 T 6     6 6 87 6 ,7    ۦ              8   ߦ                               R   .k              2                               զ              QD                              ^                     F                                  Y      D                              
                 8   q                 LD                                               8D                   Φ                                                           
      (D                                     D                 $D                   $              @   l                               <                                     B  (             DX                <  ,  ,      0   |          < d L   ` >                68 (                          `           P      p l     h    t     e              3              v                 !t              v              N              \   s                 v              'D                    t                 `   o              d   )p              p      Ft              J   a                 t              C                
t              DD                o              `   o              GD                   t                 CD                p                 C                    o              P   v                 o=                                  jo                 p   HD                     p                 >D                    ?t              F   o                 p              ~k=                	   t                    v                    N              C              Z      yy                 o              C                    x              h   o                    l=                    t                 qC                   v                 V              v   Jp                 t              r   v                  *   s                                  nC                    s                 2y              B   с              H   s              T      _                 C                                  
   C                    y              B   C                ^              X              v      A              
   rx                 
   s              C                                 F                 Z                  4   }C                                     t                               R                                  C                s                                  9                 =   9v              ^   C                   p                 C                                    3                 l              s                               Q              $   Tu                 h                 DH                  (             Hp  ~ $ ~  , t       H  @  p       x    ~ h l       4 (                            P              (                 $   fy                 x                                                    zr  (              l m m 0l l hm l l     l l  m $m l l l     l l l l m l l Dm 8m     l @m m ,m Ph  U                 v   v                            `   Cy                 MD                   Ty              x                 `b=                    s                 D                x                 Ƈ              ,   ɇ              k                 4   |y                 C                    x              n   ~              T   Uy                 1D                x              n                 x              C                 Ł                    w              Z   ED                py                 Ɂ                            R                 t   Dy              r   v                 _y                (             $ (k $@ Xk l 4k k k l     u j l k hl j dl     <v pl l Ll k j l k pk     j k 8l k m    w              d   wC                    s              y                 ,i                      l                  1t                 v                 Iy              l   t              T   v              t              r   v              Z   Sy              Wy                 ש                 T              |   T              =                    T                 =                oT                 T                 T                    A             ^M              !              Z   K              L                 ;V                                  B  (               H | X h          Ц X <   x     $ Ħ   4 8 D Ȧ          t |               z      C                                                                                                  t   ̴                 `     (                %  ( % `&        &   \& @& ,&       , l&     & Ե     D& l & T&  ˸մ                               ʴ                 PD                   j              P   4D                   Ǵ                 ɴ                                   Z   U  (             ꤗ X V  W d\   |     X X  t @v W 4X     W L   W W      V d     x 8W W W TW                      ϴ              h=                                    ۴              .D                                        =                                       &D                    ٴ              ^   C                d              N   ڴ                            r   	                 r                 [q  (             5  \ h   D        l 4   `          @ H         d     H                    (             `    $   l                  x     t   |          ة ? (                  L  H  |      ( 4    ,        h P   D  l     t    0      (             i 8i Hi i i |j 0j i     4i i i j i i (j     i i j j i i i `j i      j i ,j i j                   j   q                            PD                 B                5                 G3             D5                            ,                    ֚                 C                   3                 hC                                 
   D                   ͚                                                                               Z                    ʚ                 jC                                                      rC                                                   j   s              ^   	              r]C                 	                    q                  ܚ              
                    &              h   :D                           H   Ś                               j                    "   ~                                                          x                                                o  
            d   ;o    ߥ                 T  
            "   b   ;o    @                               =                                                                       ť              ^y                  
                 d   Ε                                  t   ӥ                 %                                             ^   h                 r=                    ƕ                 Օ                 ǥ              p   ? (                d: : : 4 h: `: x: :     |: : : ; : : :     : :  ; : : : : X: \:     : : ; ; :      
               ,;o    U  (             F G G DG LG 8G G ,G     F F F PG HG `G G     xG F G tG G G G XG p     F dG F F \G     V  (                  Ĥ h 0  $ L      Ԥ  ȥ   \ (     t   X `    H l         ĥ P     
  (             8     $ x         4 , p l      T ą  D ؅ 0     P      t ԅ  ȅ  ~ K3 (                 $  p           \ l , 8  <     d  x 4  P   , (      (  0      f (             xf4G H $, a b b ) tc     r G pb b l | q     `J G ; lH db l d P? a     G `i F b b H	5                 G              v   KD                    7              
      n=                   [                 g              z     (                H   $         x `   L (      \ d  , 0   X         t        (             + < ; | : ; 8 < ;     ; ;  D< ;  ;     ; < ; 4< < ,< < ; $     <   $; @< \<  Gb                t                                     ~C                                 C                   q                               8              T  
            j@  ;o      (              xT T tT HT HC pT B TC     4T S `T C C LC      B LT T C 0T   T      A T T B XT       
               ;o    a (                 V U ,V U U $V U  V     U U U V @V U U     DV U pF V 0V <V U V V     U U U U TV                         3: 
                       D:                    F: 
                                         h                 d                                                x              {                 
                 z   P=                                     m                                  v                 xC                   ݌                 ~>                 yC                                 Z   ތ                                                   ZC                                    l              v                 |   w                 \C                                  H   w                 Z              p                 D^              V   
              n   lkC                	   :                 W                 /                 #              &  k              r   v                                X                    z   2                                  q=                	   4                 H                    h              J              C             	   8              2              ^4                 ,                            d   !               ge              p   de  
            b                       T3 
            ,  ~;o    G                T: 
                 ;o    G                r  
               ;o                  f                 ^v                    x                 mC                                 t                 (                    [                 bC                                  l   XC                                               j   V              
   rE                  ڣ                 cC                                 ŀ                               P   3                                     C                                    u                 lC                   ٹ                 [                 dC                    y                 z.                 T                 4              j   D                    :              v              l)                 t=                x                 J              t  g  (             pV  hQ Q ؗ Q Q ȗ     PQ  Q Q ė Q       TQ Q Q  8Q Q       |Q pQ R ̗ Q :   (                r r s r r s r s     s r r |s r Hs r     r r 0s |k r r r s <s     ,s 8s s Ps \s 	              N   <                 X$                 :                 5              \   i                 G                 d              v   li=                   {                                                :   
             6                 vv=                              @P  ~=                                                   =                    ~                 P  /              `t                 
   6                            \                 z                 %                               T{              z                    H  n  (                      ě $ 8 T        К  {       l p     T        P t   Л    f                    f                 ~  (                 { | | { | { `| |     } { { { | h| (|     l| } Pp | @| { | 4| t|     | H| { D| P| 	T                 
   =                T              d   T                  T                 e  
               ;o    /U                                     2b              
      ~  (                 t 4     T      |  U  ̳  г |      X     ( ` @T      $U T  P       (                 x     t   |     Ȅ  Ą              ܄   ,       ؄ H Є 	b  (             	       P     $  \   p          t x  X  d     ,    4 <  S                 :bY                 PfC                   Y                    ~S              d O              ~uU              t                                     ?                               (   o                 
   S                 KU                                         j                 tC                    n                 f@C                    l                 a                                  W                 z`              ~   ?D                    Z                  :c                 g                 ^              Z   F                 I              j   U              T              n   9              A              
   ˅  (             j |    |  < d     <   `        0  ,            T     l  (             M (  x   p p       D  t         @ 0 | h  d H       , 4   { G  (                 \ L H l  L d     xL  L  T  L     L P  DL    L tL     x L    L ; z              t   tn                                   l                    NC                x              Z=C                   r              L                    ^C                    q              j   d              ^   e                                  h              C             j              =                s              BC             	       [                 <D                 i                 _                               
                    M                                `C                    S              Z                    _C                                                                                 4   |   <  (              X |  0  < ,        t 4       @  ` D  $ ĕ ȕ x       Ė |      TD 
            ^;o    2                    L  
              ;o    cH               T                 j7                 T                     T                 U              v   T              T              UC                   T                 T              8                    8 
               $      | q  
            o  ;o    yH                J              |   e              *   Be              X!e              ne                 ?G                   Ce              
   6e  
               F                      V  b   >               J< (             $ TL DL L K ,L 5 tL xL     LL XL L K L L K      L 4L `L K K L dL L lL     K L K 0L L ʸ2                    ^              ./                 <                 7              "  j=                 Q                 "                 ,                 M                 0              =                 -                                             6=                              d=                                 j   Y  
                  ;o                     p              ,   =                                     }=                                 W                                  2 (             o&	 t  \    L     l     8  |     (  d ,   0  <      `     	޹              &zTC                                                    zr                   F                                  V              y=                                        =                                  t   `                                                                                  =             	   	                    *                 z=                                    =                                                  *                                    T   P              \   AC                    +T                 NS              *   .X                  W              PU                 ^_V                 J              WC                   vP              (   TV              P*  V              D   sC                7V                 U                 (   W              J                .   L\_              r<W                 W                  VH                    U                 trP                 W                 T"I                 PT              N!D                   T                 =                    T                 T                 xU              T              n   ~T                 w  
            &                        2D  ϫ                 (  (             $   8  @ H L x      0  l   X       ̵ D    \ p P     $ Զ       b  (             D4     H  <        H  0 P     h   l              x | 	0 (                |            p   \   d      h l            X  x      5 
            b   D   ;o                                      (  4                    .  (                  0 ,     `       (     l     L x               \ t    8               (                 ,    D      | p   L      H  > X ( $        t     , f                 hd                 f                    f                 Zf                 f              ^^7C                   f                  r;C                 d              0      C                d                 RH                    f                 @f                 #:                    (:              (             	] L] ] ] l] ] ] t]     ] ] ] ] ] lR T]     D] ] ] H] ] @] ] ] p]     x] |] ] ] ]    Y              S                 ,_                    Y                 @C                   L              (   Y              <  Y              >   Y              dS                 SC                Y              lR  YC                   S                 (   S              ^  \M              =Y              C                    {S                 f^                    YS                 OC                    Y              x   +M              =                PR                    C                   >M              T[                               z   V              @      V              H  S                    oC                    SW                 V                     W              5W                 {=                    W              @m=                GM                  j=                V                 v=                `              (  V                 =                    V                    =                    V              VM              p   =                   V              v   jV              v   `                 =                `                0M              )D                V              MM              
   `              $   TW                  XM              n   f7M              2`                 \W                    Me              r   fe                    e              
   qe                 e                    KC                    e                 Ve              <e              re                 hVC                Oe                 e              "   e                 r_e                 C                    xe                    he              `  LC                    e                    e              D      e              GC                   de              xe                 Z`e              |   e              $  |=                    e              ~2  ye                 HC                    e              "e              |e              e                 0   e              hAa              D  e                 .f              e                 df              e              0   -a                    2a              |   Ff              e                 f                 =                    e              <   e              h  c              e                 0D                   e                 >c                    f              t   c              "      c              |c              Nca              x   d              f              pP  bH                G             G                G                G                f                  df              f                 ?C                f              bB  f                 "g              r   JC                f               g                    H                f                    g                 f                 f              f              "  f              /C                    f                       
              L             (             |4Y <Y  Y X @Y Y / ,Y     X X 0Y X X X X     X Y Y X DY X X X X     X Y X Y lX h	  (             ( 4   l W  h       L   p   X     d 0  `   X         x d H tC d" (                ; p< ; < ; ; ;  <     [ < H< ; h< ; $<     < << ; ; (< ; l; < X<     P< ; 8< < ; <   *              
	    4   ܈        @ ̈ ( D     Ȉ H     Ј        <  0 8          (             `	` H L T   Ȭ      $ $  `  | p         \ $  L  	     t    4    e  (                     p        <  x     ب      $            , ܨ Ԩ Ш                   *                                                      f=                                 \  /D                                     D                    =                    #              =              $                                                   8              ,                    =                                                  X   *              $                  d
                               6=                                     =                    F                 %                 6              B              p     1                 =                +              $              p                 *                 
   /                 $s  (                 L  d ĝ x        X    ` <       , ȝ   D  (      $ h 4       ̜                  .C                                 $                                                                                    MC                           >                 r                 8   .ݜ              vEC                                 8   9C                    Ԝ              P                    )C                    	                 F              z                                   6              4                 ^C                                    
                                  ZFC                                     l              &                    V=                    ?                 @s              $H  >                   s              0                h  U                x                 p                                  m              7H                   }              *  |              f              `   (                >   >                   w                 %>                    s                            \  ?>                                                                                 6                                                0   L              8                   
            h  ;o                     ɟ                 d˟                 PC                                 H      П                 X=                              ^=                                  xP  ڟ              $      Ɵ              "                 ǟ                 =  
            V   ;o    ȟ              x   =                   ۟                               j  ܟ              x              n                 ݟ                 F              =                                                *                 x   Rޟ              H                                    `   
              ҟ                  4 , 8%  W O  XX Я   & P @ h t%   & 0  `  p  pR 0   (  *  Dl   | T D ̗ HV \p 0I @p    [ p l. (p }  {  } |[ `  @h ܮ 8g  <   ` E   H  " $ , x l  X   d  T   p @/ W  g k r u   ` D  X  ) d  0 l  	    )   5 8 5 LF (R 4] b X $q 8 <v  @  ,[ L2 T  (I   T  , D   `   ˸`&	              $           ؿ	x	&	             L $           ؿ		l&	              $           ؿ		D+'	         	8	  
            0          Ι  (                 d= < = < < > (= h=     = ,= H= p=  = = >     `= = 4= \= = L= d< = <     t= T X= = 8=                   6N  AG                                  &   ^H                Q                 F              d   IC                    x                 P6C                                 m^              "   q                *                    <              *                    nu                 ,C                                                     bv              ~   CC                              |                  r              l                  (                            ,8  =                                     To  
            d  ;o                  6   H                                  "                       H                                     |                              0   Xl                              &               \                   c  (                        $           |      t    ,   (             fe              (   Ld                 8ze              $V  d                 d                 V?                               (j  a                 4                 dC              "   k                 ?                 `"             RM                    K                              >  J              >Z                                                $E              0   =                   W                 =                :              .                 :=                !                  ^   m              |     5                    =                    B              n   =                                                  "8              0   N              f@D                	   X              .                 =                y                D              
  r              &  B                    =                                    =                Y                                  H                 M                               8  2                                  6              $$                H                   a                                  <      H                ³                  <C                                    H                              "                    2              &                        ʳ              H                ȳ                               t  r                  @߬              <                0  ~e                 je                 De                 .?e              T   4e                 =                e              *   Fe              
      ;                  s              ,  ,   I              6   =             	      h              ~p                 }  (             (	H  4 ̇ 8         D ܈ T |           P  ` < ȉ ؈       P Ĉ Ԉ *              &                 4     (             @		0 P1 Q @R H0 L1 Q R     p$ 0R 5 / P0 L0 0     0 h0 TR  0 ,0 / $0 0      p0 x0 00 /   q                 S              V=                    c                    Ȣ              Y                 2j                               f   ɢ                 =                    O              2,  h                 k              J   =                !              &                8   =                    p              a                                  e              *   6   V              0     Q                     =                 ^                               r              ^=             
   q              4   u              ,  * 
            |   ;o    9  
                       l              $   1              4L                 4>              l  6   J              @   ]              XA               H                [                 C              b   W                X              n   V              $   `                H                                m                a              5C                    q                 I              (   R                 H                 H                   r              <   ~~              2  =                    S              6                 {                                  H   p              `   ϩ              \                 ,   ѩ                                               
  =                                       =                                  2                $   =                                                    =                
                 J=                    é                                2   ɩ              Vک              =                                    ҩ              :=                                                      
©                >                    ĩ                 =                    ֩                 6              l  F   ީ              F                    H                &G                G 
                    G                G                G                |': 
                      :                    !                  $                     u               
 L                                                                                 G                                              G             	   G                G                G                G                 G                G                 G                G                G                G                G                   G                G                G                G                G                   G                G                G                   3C                |              F  08                8                                 L  (                              H   bH                {                                                   )     
               ;o    M              
=                                    =                    Y                H=                    q                 =                   '                 @              4  =                 e                   S              &  X              *                 $   @   ǫ              6                \                 ̫                ګ              ٫                                 ֫                                  B                               C                                    H                                 .   &  ߫              8                    *              <=                   Ϋ                                             Z   :C                    	              $   ۫              (      ܫ              @                                 T)              n                 Đ                 0=                                 =                                   =                                     :=                                  (      Ր                 Ӑ                              $      =                              Z   !>                                 0                 2                 Z      2                    =                    8              Ґ              ,   g                  =                                  J=             
                    d                    =                                     =                #              r                                 Z                   4              48              ,              $              B   }  (                  | |         L   p < D X     \   h  T $  0      H  P $ >
	s                ɭ                                                    ̭              ,   (                     H                                  2                iC                                  &                    <   ѭ              TH                              T                 H                            H                ܭ              *                 H֭              "R  ­              HvC                                 >   έ              0  ӭ                    
                   Э              "                 ޭ                 ۭ                  D   ŭ              >  ԭ              )                G2                                 (                 t      8       p 0     l      T @ `  $            ,   l    Ǫ                                0                 H                                 "                 *   DC                                                     H                           L              V                 D   ت                 ɪ                  
            2   4  ;o    8                                 P                    ê                               J   V              &              h   ͪ              *  H                                 D                                    8             
                   H                    Ѫ                 "                H   H                    Ԫ                                                  Jd              P   >             	   R                 HW              <   Z                >                   \              l   K              \  5              u=                   l              x              h  ]                 6D             N              NV                    7              =                 m                J              2                    r                p                y              6   (y                y                   y              fy              &   y              >   =                y                 w                =                   y                 y              :   =                	   y              0   =                y              f   y                 y              Vw              $    w                 6y              b  >   =                   y                    =                   w              &   y                   (              s `# !  # 8# (# " " t"      # D# 0# " H# $#     " " " " P# # # " #     " " " x" # W 4 (                 l $ h                           x           $ 
	                 w              :  8y              "   j                 {                               0                ^   uC                   ó              L                                        P=                                                   `H                              X                                 r              "   f              >      ^                    y                 =                    [              &&m                   ]              "                 B                    4`              VH              `y              (   =                 w                Ly              .   y              :;D                   y                               N  ӵ                                 H                              n   ܵ                                                                          ߵ              v                0                H                                            2                $              Q             fP    (                   P (2    X     L 8           X 1  P 2 d         x' p2   j     .u  
                Z;o                 *   ̈              (   X   ҈                3              Z   a              0=                                  *                j  I (             r z Hz lz z 8z z Xz z     z z z z z z xz     dz z `z Tz z z z (z z     @z  z pz 8 0z R q                q              d    (              6 0  T           < `    P     h     t   H     H ( \  8    |              d                                                 :                                                 |                <                 6                   H                                               0                 (  H                                               .                   gC                                     
              B                    H                	              <  u                 "8                    8                              F              0   :              &   [                 F              $                     =                                 
   U              R  G              
   h              BX                 =              o                                  J   g              :      J              P  ^                 =                G              "B                  "M                    =                    e                    _              ,  ~              P   p              $      =                   s                4  (              + + l, + t$ d, + ,     , + + , , @- +     D, + 0,  - d% ,  @, ,     $, , , L% P, D                                           H                <                   Һ                                                <                :                 .                 >                                                      =                                                B                                            B                      =                C                                  P     
            P          3  (                 $  ԅ  Z  <     m  0    1     v v    u  ( w     @    l     H                              Z  >                   x              0   y              \                n                    pi                zn              "                 p   P                                            @                 F                 nD  j              >   q                                P   ,̽                 &   ڽ              $   ܽ              R   ý              H     =                   ѽ              
  ս              F  =                    u                u              *  ɽ                                 GG                   ֽ              H                 J   ҽ              6   Խ              &   /=                    ǽ              l  Ͻ              l  8                   8                              ,   ߽              4  ӽ                              <   	                            8   =                                  9 
                   9                    ׽              0                                P   B              <                 &H                               H   #              "                                 "   =              @i              6  F                                (   C                                     QC                                 ,   "                H   L              NC                                H                2              $   H                              P   +              0   8                
   9                ܠ	O                 H             +   )                    H             K              L                    
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               ;o    9 
                                    J                                 *                 F   =                    	                #              
h              "                              f  >                                 &                 b                4   .              6   >                    /              6                                  .                6                      r              4   &s              p  r                 r                4s  
            l  8 HZ )              .  8                8                r	,              T  |M  
            4  ;o    .              hN  o (             b<7 h7 L7 7 6 (7 7 H7     X7 6  P7 7 7 6     7 p7  7 6  7 T7 07 6 $7     ,7 D7 |7 6 l7 T &                   iH                                                   *                4                =                                 B   lH                \              
  xH                P              L   uH                P              :   "   gH                                 p*H                 (                                             8                M:                	              &   mH                `Ɏ              ^     6                               ,  +                                  :              L  u                 u               >  H                u                u              u                 u              :     wu                 u              v     H             2   ~              
u                 u              u                 /              6   $   u              H   u                 ~              hH                8u                u              H             u              {     u              `~  u                 8                    8             $   u              <=                    u                 ƽ              0   8             8                   u              B=                u              H  u              &     
            N          ! (                0  (      ,     $ D Č    ،        @    Ȍ  Ԍ     ̌        a                                   =                    0                                 H                .              `H                ۅ              *              A              2                a                                     t  L                   4                 "                 8                8                	%              P  ,              4   6              <   ȅ              0   #              TH                  -              H                N                 H                8                 
?              .       I              :                       @                               *  O  /                            8   H              
              @                L   H                                  H                              .                   2                   8                	Ɉ              H                                            H                                                  :   t                              ~$              V  ؈              Z     ʈ              4   H             "                 &                   q              h"H               Έ                 8             $   8                   ш              (                               H                Ԉ              (                                  9             "  > 
              x;o                  ]                                   T=                                               t  @              :                                  
                   8                    Y              8                               2   $                               .
  =                                                                   	                 =                                 R=                    !                 S                 "              &  
   .                 =                P              vT  =                              &              <      '              :        (                ,        l         0  d    P  x        $    4   `  L           (  p  |  t     G~                            TL  ˖  (             v  X \ p2 H 8       Ԫ    <          d   ̪ ت |     ` l  D    {q              *   Fo              $  o                  p  =                    n                  n                 n              So              ;o              <  =                   o                  |&o              \  x%o              D   >o                o              o              f  >                    fo                 6o              ?o              =                   Do                 ?                    o              co              H     $o                 \o              T   ND                    3o                Po                     do                  8o              @   u  
               ;o    to                _o                  
              \;o    !              6                */              N0              ` (             N	, + , <, + + + ,     , , H, , x P, +     h, d, $, , |,  , l, \, x,     ,  , + , 4, <  :              8   9                     (                s xs @s s s ts s $s     4s Ds ps s ,s (s hs     Y 8s Ls s s  s s s s     s s ls s 0s  2C (             # t# @# # ,# <# `# #     8# # p# # x# h# #     |# # (# # # # D# L# \#      # # # 0# #     (                   l    x           4 ,      (      0              r              <    q              f8                    8                ܠ	q              q              4   q              v  kH                Fq                r              H                &1r              $  q              `   r                r                 tC                q              2  'r                X   RC                q                q              f   r              H                Lr              R   =                    r                  (r              :   q              0   ,r              ,   H                   ;r              ,   9r                q                 H                q              .   ,2             d                      ݬ              @              H      ,>                    ?                            *   I                 8                   8                                 
                  .              8                 |=                                 <  ,              V                *                 >                       H                                                      vH             
                     
wH             !                 
      }H                <                             2   -                                zH             4                 &                    ~H                B
                 ?~                 \~              8                   8             j	+~              ~                 
   Z~                 >                h~              :   Q~              :     P~              f  /~                ~~              F~              $   L~              ~>                 %~              H                A~                Y~              rk~              <  M~              H     _~              Z   l~              (  ^~                J~              t     j~              .   R  K~                  ~              Py~              =                |~              0  pw=             B  ?             .x   S              (L              &   [H                 K              L              rT              f  T	L              {T              &      L              p     L              Z  (/              T   (>                              N                >                                    >E                 *                "                 #              =                   %                 &              (                    "   (                   )                 Tb              d  =             b                *b              ,   ,b              t)b                 1b              .   b                 =                   U`              L   8b              0   dH                \b              Z    >                    Db              :   Qb                5b              7b                 8                   8                +b              H   =                    a              &Fb              8   =                    6b                      b              H   &>                    b              6     
            4   ;o    8                    rb              (   -b              2  Vs                 Ys              =                    ds                  s                                               &                 ,                        (                 
  :>                                                                      f                   {C                                  @   $                V  Ȫ              s  
               ;o                                   T              
  *               <|              :                  jH                  ԁ              V                 H   M+y              H   0y              f9                 9                   a              **Y              
     >:                   :                ·              z   v    
               ;o                  ny              @   qy              :                :                xy                x              8   ,   ց              	              F  H                s                 0                 JӇ              d  ty                  0   6              h  .v                 
:                   :                i	މ                 >                                  J  :                K3 
            x  ;o    J  (             	 |               h  p              x                                              >                $                 R                                                                fH                              H                 a              (   a                L   >                                    a              6  b              \  s              4  s                    .s              ,   l  (              d  @ (           T p          L H P l   0 4       D $                  b2             ZL                 /2 (                    ,  \          ` (      D P  4      H      L        4              D                "                >                   '              ,   (              H                                 `   >                    8              0   z-              `                *->                                  *                    Z     H               }              2   9                8                                    OH             $                 ,                 >C                    ׃                   8                 8                -   ̃                                                   &b                  ԃ                            
   "                 v                R              (   y                              p                >                B                                      8                    8                              ǃ              ݃                 H  RH                   ʃ                               4                 Q             .H   R                S 
            T        /             B   r              $       >                    Xs              4   Rs                                            h   2                                zz                   5H                                 
                    ?3                                 
                 P  n                            >                 .   8                =:                                  6                $                D   K:                 H:                                               v    
                                    o                                                                             F  j   oH                X              \  8                   8                                              h     8                    8                                 sH                                               Z$                 27                2              :  #>                4              8              6              n  9              
  =                R                 >              ~  ?              6  j@              :~1                 jB                A                              Ls              (  '>                    3s                                                P0H                           <  }                   ~              AH                              h  T              D     
                  K              >     L                v>                   T              L              0   I              J  L                K              :   h   <>                 L              X   Fs  
            l  ;o    :L                   L              :   8>                   L                2L              >                0              T              \pT                T              :  >                   b`              8                    8                    kM              =                T              D     !s              >                us              @s              T      ">                    >s                                (     (                 |v v v v 4v v v v     lv $w u v v v v     Hv Xv Lv v v v  w  v ,v     @v v v v xv     r (             	t  \ (    4 |      X  L   8     D  ,    $ h @        H  <                       (                p 8 \  X  @ T        h , H      t < (     L  l     4 d     	              2   4  (             0  l      h     H 0      p      L X  | d \ D        $ 4   4 (             H	(D DD ,D XD Dq HD X8 DC     pD D D 4D D 0D PD     D \D  D dD D TD D D D     D $D D LD 8D }C              &H                 )   Z                `H                \              N              B   <  pH                a                T                r              d              P   _                 j              ~0e                 p                 h              J  8             	   8                    U              v  >                v                               v                        y              B   $   8              p  2              4   -              E              >                 8                    9                d	4                 \nH                !                a              R]H             	   	   9              %              n  H                    D              B   
>                   >              v   Ji              f  h   @              B  =                M                ?              2   H                    F              :   L              n   l1                 K                HH                45                ThH                fO              P              Q                 ) (              \ ^ ^ \ ^ ^ ] G     ] ] ] 4_ `^ ^ \     \ $^ ] ] |^ ] @^ ] (]     ^ ] ^ \] _  }
             /s                 @  $s                 Zs              Ms                             V                               R             R   ": 
                      0 :                P 
            X   D  ;o                  D   %H                                                                   4   ,                                  ~  
                                            8   ,                c                `              ,   d              :  YH                re              dn  h                 R              t  k                 (   m              <   p                ^H                  o              P                 *  X                        8                {              \  PH                pu                \H                f                 N              @qH                    x              
b                              _H                ~w              <                 >   R8                   C:             
                 N   8                   8             -                 4   t              &                 ^                 L  eH                              .                                 H   (              X   &                 $              <                )              D   T  >                   3              "                 :  -              "                	>                   .                1              .  2              
   E              84                 Z  7              P   9                +              d  |>                @              ~I              D   (     
            r;o    8                F                
   Z              $   r                K              $   a              "  )>                N                 E>                   P              Q                                \                                                  *   SH                              V                                                  $   =>                                  ,  j   H                                QH                              F                :                 :                d                ^                 4              h  VH                              8   P                
                                  N                                 N                :   n              :                               V  XH                              6                 "   y                 ,                            V              Z  >                                  1>                                  n                   C>                                                     KH                                  
            |  ;o                                                      >                                 `                 (                                                      r  ~                                                                             
                V<                .                \                             <   ;>                                                                            T;              4   ?              9H                 A                 D              h  E                F              `G              jH              2      I              ~   S>                    K              h:   W              BX              69>                    Z              2   ]              X^              N   "  a              >  2b              F     c              d              h  ne              P   t   f              >             
   h                   B>                   j                k              ~=                   m                     n              ~J   3>                p                s              
B  v              w              G>                y              b  z              6  5>                |              t   .>                    ~              >                                                    U              8                   WH             *   "                #              N   $                   )              ^  r*              P   X  +              ",              @  7>                	   .              >   4   >                    0                 ^  >                   7              J>                    4                  5                6              x%                 O                ;              8                8                t	>              ?              0   =                 A                 B              V   *>                @                 G              *  H              H   I                4>                    K                C (                C xC `C C C D C  D     C dC C C tC C XC     C C C |C C C PC C C     C pC C \C C 	 (                 $ t           ܿ  ̿    ؿ             Ŀ      x h   ȿ       (             \               x t   P `     4  \  T          h                                                               `  |H             
                   bUH                              F                 p                 b  |rH                `                                              4                \                 6                 4   N(                                               *   2                            T  M>                               @   #              V   NH                              4   LH                %                               (   $              Z  .              ^   6              F   <              .                                                  f                 F>                              2x                                  j>             	                    0              ,                 2                B                                 v                 B                 d                  +>                                                  |                 =                                                  4                 P  *                                                              B   2>                              5              f                                                                    !                  
               ;o    9                   %              &                   '              ,(              X  )              "   ,                 -                 <H                4  /              2              >3              H                5                
   6              ,  FH                8              .      9                :                ;              $  $   =                    =              d   IH             ?              >@              H  6H                B              0  C              $  D                I                b1              H  2                3                 d  4              N   l  5                :              d   BH                <                 H                    >              @H                @              2  A              &   F              J              |K              "  rGH             :  M                 hN              O                P                 HH                R              NH  S                 >H             U              r  RV              T   W                CH                Y              Z              H   0   [                 \                   ]              4                    ;H                               R  TH             
                                 >   4H                              ~   2H                              0      =H                	                8                   R:                               X                H                                                    z                               ?H                                              *                j                 B3                    ?:                                                t  EH                "                 #                d$              r  :H                &              '              R   (              )                .8H                +              V                  f             n   +H                                               9                                  f                 $   =                              t   H>                                  |              l  "   $>                                                                  >                                              ,                x(              ,                "\>                                  `                
                                                                              &  ]>                                    <              j                  !              v"              6   I>                
   $              P   A>                    &              N>                    (              V)              h   *              `  +                ,                  =                    .              1                2              \  3              tH                L5  
            XJ                                   *F                j             b  
                               &h               t               J                   PW>                                     ,                                          D               zg>                             f#             H                                                  	             :                  /             h     *9 
              ;o    7               >                	   %             )               <s>                    ?             D  ,                          
               ~                             N  $             n                  B:                   8                l	                          "                                  Z@:             -   8                                    <             L8                    9                	             d   	             4   
                          K                  :v               p             X                  V   *                f                    6>                             4                                  x             \  @             $                   !             Z  i             N                   F              |  
                
                  
             xO              d   h  Q                    H                U                W              Z  Y                4[                ]              _              &i              ^                                    >                                                $  P>                                 L                               9               (b                                                          B                  
U>                                 D                                 q>                          @                   7              H   4   D>             6   9              -     :              :  @ >                 <              P  T=              .   >              T&" 
            j   ;o    B                   F                 b>                   H              r  rI                (J                 K              T                                    
            L                          >>                                    
            :  ;o    8                                              @  0>                                  "                             e                  X                    
            2                      P  2k              *H             u              p  .H                                   /H                              D                     (                                 8                      1H                              |                            hh-:                    P:                ,,	                 <                0       A:                    1:                              $                  x                 ,                    JH                                              R              VV0:                   _                \                #[                X              ,H                X              \  8                    8                	R              Q              ~   N  X              n)H                kX              >   X                  *   aH             	   +Y              
   'H                Q              t  @+:                    ):                   Q                (H                 X              0   $   Q                   X                6N              "[              
     &H             	   	   X                 ,   	K              jJ  $H                 Q              X  ?t\              X              B      R              F   O              B   nX                jXZ                 .:                6:                t	R              n9                   E:                	X                Z              2     \              fR   ^              `              b              d              R      f              H  h              T                                    D                       >>                             &                  G                          H                  6                8                                           <   *                    :                   9                             9                                 X                "   (   (             B                >                               z>                    ,               &>                
                            N                f               x               :	             ~                          R                   f                                              `             >                                 :                9                                                                 r2                              ,H                                            H   >                                               V                               Z                   (             p                (                                  
   p             .                                   '#             >>                   )#                >                    +#             ZT   /#             vV0#               &1#                2#                3#               9                 5#                >   6#             t   >                    8#               J9#               <#             T   R   =#             r   >#             ^   nv>                    @#             H  A#             T   B#             j  H                VD#             f   E#             H#             d   ~I#             &  J#               K#               L#               P#             0   Q#               ##             X  $#             8     -/ (                 x    h         l                            t                 0                   .                               P                 .                                               $             pT>                                 j                0                             ,                \                                                                                
             @  Y  [>                             :               c>                             Z                  l5             >.5             B  t5             T5               >                    5                5                  5             5                ,  5             d  5             "5             &  >                    5                5                             FH                P             l   H                             x  G                @             l4:                   :                $,             |                   H                F             ^             dJ   	H                                 n               L     H                 	                JZ3H                :             :                                `   4   H                                                 >                                                          x             4<             
                                 9                   :                                 j     :                	:                                                  Z                               ~             n   *H                 
            z~        U             [             Tb   \             ]               ^               _             <   G                6a                  b             />                d             ^  h               \k             w>                m             p             "^q             Pr             j  }>                    t             2      o>                   v             \      w               x             |  y               |             r}             ^     ~                          (     
             >   x
             b   
             _>                              2      ^>                                ~H               D                              p   ~>                             2               `  	             xI:                    2:                N:                	             hz>                                                &   \Z>                                  L:                    /:                             r>                                   0                H
                             $                `                   #                $               `>                &             P                                                (             D                Y               xQ>                                T     H                             <               X   Y>                                                 >                 X>                                                    j             h                                d                                             j  V>                                 L   i>                                          $j>                                x                                           z             ^                                                            ,             db                 t                            LB                  r             |                                                        :                    *:                             ^     u>                                <                               8                X                   N   &                              <n             d               Q:                9:                                               *      #H                             2                 a>                                 p  b              8                 ~   Ƽ              n  :                    J:                   y              p     ~                   :                9                   u              b  9                %   9                 ;              0ǝ              $                 r                 ^   <   w                H                R{                
H                H                              <   ,                            VD   P                (                 G                H              T                "&ɼ              Nua                ʁ                  H                                     t>                                     t              2P9                   9                :                                  r             `             f   @                               .               \  f>                                                r  L>                             4                ~  R>                                 O>                                                                                 H                             h                Z                  Px             >j                               d               k>                                 d                             P   8   n>                                 $               l   4             <                                    8                    :                             X                \  |                          8                ,    $:                    ,:                                          D               P  H                                             |4   %:                :                                   4                  L             p                H   8                    !:                              j                                 P   >                                                T   "H                             |                T             d                T               h                ||   l>                6                                     t>             6                                 @                X               <                   \               `               @                 0                          p                               ,   9 
                      9                                 td>                
                Xl  H                             j                    e>                                 p             h>                                 (   y>             
                d                d  x"               :9             n  G                ~   <9               =9                >9                ?9               E9               F9             P   G                H9             G             J9             2\  K9             dG                M9             td   @ 
            4  ;o    9                   Q9              R9             >   S9             d   T9                  9                 9                    W9                X9             v  JG                3             b3             3             d   3             "|  >                    3                  >                    3             3             >L  3               >                3             v   3               :>                    3             0     3               3                9                    9                i	3              [:             (   6   \:             T   8]:             "a:             N  b:             hT  c:             d   d:                `G                f:                g:               h:             \   i:                j:             jk:               l:                  9                   9                	o:             v  p:             <  G                dr:               s:                w:             b   j9             9                   z:             ^^   {:             F   |:               G                ~:             (   :             `   p9                9                D	:                3                >                    
3             3             3             (   2                    3               3             "$>                 3               G                2                3             ~   (  3               4  9                9                	3             >  3             .L   3             83             23             h  V9                    /3             t   !3             V  "3              ~#3             :             <   :               :               :               >                :                  :                 :             j   B   >                    :                >                D9                   9                ,g	>             ,G                 >                >             X  9                    9                >               >                D   >             |n   G                >             V   R>             .@  >                  G                >             ^  >             F   G                >                >               G                >               >             $  >               >               >             G                >             N      >                >                9                   9                >             V~  9                   9                   >             ^t                 >             j   x>             :  H             *PH             \H             (   UD                H 
            T  ;o    YD             8                [D             R\D             r  9                9                   _D             t `D             N  xdD               eD             F   fD             n     gD             D                       iD                  nD             t   p  oD                                qD               .G                sD             tD             uD              vD             wD               $xD             v   yD                                {D             
  |D             V   G                l   ~D             f  D                  _1                `   D             r      i                 D             vG             2  wG             8  xG             t6  yG               9                    {G             L  >                   }G               ~G             )  G             ~G             
   G              G               G             X   G                6G              v  G               G             G             T  M 
            2   ;o    9                   G             
   G             FG             J  G             ft   G             G             T   9                G               ,9                    G             p   H             2  H                 H             
  H             P                 H   H             B> 
                  d 9                    H             8   H                d                 H             *  t                 H                H             
H               JH                9                :                   :                   H             R   	                 H             B      H             "  0   H                 >  H             H             >  H               \H             <   H                :                9                L	H               H             z  H             *                   H               M                M                M                M             M               M             (M             F   M             (   M                M             jM                M               bM             ~  @M                M               M                M              B   M                M                    M                 M             t   H   M             (   M             t   t  M             8   M               tM                M                M                M                M                M                M             "M             >PM             M               M             vx  M                M             	   	   M             M                M                M                  M                M               M             5     M             <  M                \2               G             ^2             $   _2             xG                za2             :B   b2             JG                    d2             4*G                tf2                 >                    h2             i2             :  rl2             v     p2             q2                Z2             p   >                 |                l     W                 0   ͗                 0   +                 {              X                 k              (m                                    g                 w                 D                ~                   (              8                9                   J              L   <                9                   9                	C              DP  l              0             p  0             N   0             0             4   "   >                    0             0               >                 	0                  X:                >                	   Z:             &  @             b@             <   @                9                    @               @             (   8   @               rpG 
            h     ;o    @             d  @             p   @             Z   X2             	   	   @               >                    @             <9                   @                @               @             \   @               9                   @             B  9                    @               @                <9                    @             p   d@                  @             4  @                @             f   @             T`   9                    @             `  9                    @             @             x   v1             4  >>                    x1             bd  y1             Tzz1             (   {1             B|1             2  }1                ~1             *   tx>                    1             >   9                   1             z     1             |G                v1             "  1             B*  1             2   s2                  t2               u2               $  v2               w2                G                ty2             f  G                   {2               |2             (   G                ~2             @   G                    2               2             2               2                9                   9                D	2             @j  2                 2               ,9             G                 .9             ^  ^/9             09               ,19                29             T  39                  49             h   59             (   (9                   9                89               5             *   5               >                    5               5             B   5               5             v>                    5                5               5             n      >                5             <@   5                5             5             Bp  5               3             P   3                3               >                    3             b   3             V  ^9                 3                .3               3             xb   3             L  3                3             |   (     save "valentine.s"; gf     M592:=ModularSymbols(DirichletCharacter(592,[1,1,6]),2,+1);            M592 	L	@                  D   "  T ' 
   L'                     .2                      L                         =2       62 
            P             &9                          P       %      P               %      P  22       %9                      L                                    P  ח                               L               `H \_                 T2       !   P          $9                      L                ]         F2       9    Print(M592); Symbols32                      L                                  O   P                 7v           P  8       (9       I 
   D592:=Decomposition(M592);  `             Z`             |    `             RW`             F  z`             ^  `             =`             `             *   `             K     `             2     `               w`             K`             :     s`             }`             "   r`             .   2  M`             <  e`                  c`                  |`             $     `             P     V`             \   `             .   `             /`             *   u`             0`                A`             0  `                `             `                   p`                `                 `                N`             -`             `             @   `             H  `             ,   ,  q`             S`             4     `             `             L  6                `                R   `             L  y`                U`             l`               `             "C`               m`                
  _`                `             'Y             >  ?`                `                h`             :  
`             X  `             `             *   9`               O`              &  `             H  H`               
   b`             `                !`             &  Q`             B  5`                ~`             2  R`                  j             J  j               j                 0  j             Ld             7                 e             7                d             d                d             .   R  d             |  d             .   d             d             d             d               d             <  (7                 d             2  d             d                  6                d                d             d                  d                d             &  d               d                (  7                d             8  d             d             d             47                d               6             T  d             d                   d                "  G                d                V   d             `  :  6                d                >  6                e             r  6                d              z   d             B     d             n  e             V  d               6                d             2   "   d                l  d             d             :   e             d             d             8   R  e             D  d                   d                  d             &   d               46             
   d             2  d             b  7                d             d             :  d             l  d                d             d             P     	e             n  l 
              ;o    e             2@  d             *  d             T  d             8  d             pHd             h  d             H   d             R8   d             f~  ^7                d             ^                   d             d             d                H  d             H                   f  Ɗ               
                             8   ӊ                $             x               "             h             x|                                            1               9                                 	                  N'             R  ̊               ʊ                T                P+                T             b   U                 U             0     T             b  7U             &     T             8  Pp              
   &U                                 T             X  w                    U             l  $U             4  U             >   T                T             +U             h  T                J  yU                U             ,   E              
   T             *  T             $   {                 T                T             &  T                              	   	   U                !U                 L7                T                 (  T             
   U             *    U                T             
                    T             0  T                                 $T             $  T             "     T               T             5U                U                   T                T             &     T             (  t              "   /U                U                T             &  
U             $  T                -U             "                       T             6                 T                                T                T             T             U             
   T                7                ,T             $  2U               T             ,                T                              P   U             }                 U                `   T             T                 U             T                  T             (  6U             V  T             ^  T                 3U               U                $  T             *U                *                   T             
     T             j             x  n@j                Z   |j             j             j     )j               oj             2   Dj                $j                  8j             V    uj             \j               Vj             h  
   j                j                  Sj             H  +j             8   :j             2l  ^j             V  j               &j             tj                0  [j                D   j             j             D  L  -j             gj             L  xj             ,      }j                4  j             j                    6j             Lj             6   j             *     Bj             P  j             6   j             j             j     4j             2  j               j                j             mj             Tj             c               j             \  sj                Ej             |B  j             fj             Mj             j  j             Wj             0   ,j             r  j               lj             :   q 
            X   ;o    j             tj               pj             4   *j             Yj                _j             !j               vRj             rwj             l  ]j             &   <j             X  5j               dj             `j               j             Gj             p  ?j               l               b  l             x                 Sl             bl                  Ml               8k                 jl             D   dl             
  l             ]  l             \  r                    hl                   l             8   |l             l             F  (   l             6                    	   al             Jl             |  Xl                ;l             H  7l             zl             l                                    (  l               /l             
   K   wl             T  l             L  .   l             6  ,                   >l             p  `l             d  l                              Ul             :                   l             .                       _                                   Al             ,  l                yl             8   5l                e                     ll             @   ~                    Vl             y                 xl             H  bl             6   Zl             P   f                 l             *                    fl               vl             f  l             2  gl             l                l             z  3l               kl             el             N  l                Gl                =l             l             N  [l               }l             xcl             n  Cl                   l             Kl                l                 l                                l             4  ml                                   l             1l                  8l             N$  Fl                d   ?l             l             D  Hl             <   zdl             >  {             X  p                p             { 
                  ;o    q             D  p             a     p             *   *  p             N     p             \  p               p             0(  p             *  p                p             p             p               p             N   q                p             d  p             6   D  c             Dp             p             p             p             ~  p             p                p             0   p             B  p             P  p                p             .   p             (     p             p             .  p             h  p             ,   p             l@   p                p             q             t  p             &  p                0  p             p             .   p                   p             j  vp                   p             p  p             p             $   p             D  p             @  p                  p             -                 :p             F  q             l     p                Z   p             p               p             6  p             q               p                p                p             p               p                p             P     p               p                p             T     p             :   R  p             :   q             G                               ^                                ,   ^              4S              $                 e                d8t              n  ў              ,   l+                 AW              4   Y              vh              J                |     Y              l  $              (              0                   n                `   ߋ                W[                            d  P[                    ƹ              B  ͟              P                L                @  @  :                s              d  [              "   ^              D"                   `              F                                  @     rS                 V                            z  	                 ^                rM              (  j  ^              h  vS              D  *                 >  _              >                 H  $                QR                  Z              U                 f   h                    6             l                     ^              4   W              
   [                            <  R             l  R             H  R             :  ZR                2                   R             t     R             0   S             R             >   R               S             R  |R                 S             $   R             x|  R             R             S                h   b                   S             |  S                                    J*S               R               x'S               R             Z  R             R                R             R             ,                    R             b  !S             2   r  .S             R               X  )S                    S               R             `R             R             S             R             r}R             z    R             r  4  R             R             
   dS               S             8   a              "   R             4                    DR                f  -S                                  S             J   7             ^  A7             >                    7                7                7               l                 7             x7               7             Z  w7             <                   Zq7             L  7             ,7             >   l7             P                   7             :  8                   rk7                              7             0   n7             ~  {             {             ~  R  {             n     n{             {             6   {             @   {             8   l  {                {                    {             S{             h  {             {                Z   {             {             p  Z{             H   j  {             2  
   s{             d8t{             f  Y{             X  {             {             2   &   {                {             h{                
   {             <  {             N  {             {             z     T             ~  {                {               {               ~{             _{             P{               a{                }{             {                4  u{                {               {             r  U{             $     {             $r  x{               b{             >   {               
                 {             V  \~{                (  {             K{             {             @  {                 `  {             0  [{             L  `{             v|{                 N  h{             {             {             L  O{               z{                D  q{             <   {             n  *  {             .   {             {             {               ^{             {               {                4  Q{             0  lV{             .  {             
   R{             J   7             ,7             X   7                7             |  7             7                V7             B   7             d7             x  7             v  7                7                            Z   ӂ             X  ̂                            L  ؂                             z             R                  5               ΂                 X             >   V                             Fт                            >               6  |  '               L             zE                  8                "                ,  K        c   P  2     42                      L                         9          P  ʗ                       L               p          '9         P  9                      L                         9          P  	9                              L               D $         0       C      ;2       4       c   P          8                      L                         9        9         P  8               ?2                                                                  9    "  M                            P  (  `           "     9    \1     P     9                    %          X	     ˸8             H                   %                              9 
                      $   V           %   9 ,                                                                                                                              ] (     d^                9                      L                          Z     8 
            $         $   z              	                                 8          <                 <                                 H                   o        9           (                                                     L2 
      ,                  <2 
    L            $2          P          
9                                         &2          P          4       9                    9                 -2       9                 
                          9                                 9                                 <         t         !9       %   8˸B2           " 82       "9 .         $          P      o        %       p        8     m             q        X     r                        $     s          ' "         H f     0   h=     g         a     h        Pa     i     0   t'     j                                                L               L                  %   P                   9 
                      8˸#9                         $     $       G                 l 		H                      L               `. \                                L                          12          P  O2                              L                <         G2       I  P  >2       D2                      L                                 E2                      L               P ?         S2          P  K2       W2                      L               L ,                 0         P  02          P  @2               92                      L                         u                      L               8          3        	  P  Q2                              L               H D         
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*                      L                0         %*          P  )       )                      L                         *          P  )       !*                      L               P          )          P  B*       *                      L                         *       +  P  Q*       *                      L                D         **                      L                         *        *                      L               < ,         $*       	  P  )       *                      L                         2*          P  *       )                      L               Ȩ X         *       S   P  E*       *                      L               @          9*          P  *       z*                      L                D                                L               H P_         x                       L               , H         h        O   P  ߗ                               L                |_         )          P          7                       L               ئ X^         )          P          )                      L               x ^         )       /   P  )       ̗                       L               $ p         )       A   P  )       v                       L                         &/       Q  P  )       )                      L                         *       M   P  )       )                      L               T          )       }  P  )*        *                      L                         )         P  *       )                      L               ܧ          *          P  *       *       9   P        )                      L               l          )         P  )                      L                @         )          P  )       *                      L                         )       7  P  *       )                      L               ̦ L         )       !   P  )       )                      L               d          )       I   P  )       )                      L               Ц          )    J      P  )       )                      L                          )       s  P  )       )                      L                         )       '   P  )       )                      L                         q*         P  )       )                      L               ĩ          )          P  )       )                      L               ܦ 0         )          P  *       )                      L                4         )          P  )       )                      L               L          )         P          )                      L               ( X\         )       A   P  )       )                      L                         )       k   P  )       )                      L               p ا         *          P  )       *                      L                x         )         P  )       )                      L                 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T         	          P                               L               $T 5                  P                               L               ,S hS                  P  %                             L               8S T                  P  /                             L               S T                   P         <                      L               T S                =  P                               L               HT pS                 {   P  X                             L                T `U                  P                ;   P  s                             L               w y                I   P                               L               w lx                  P                               L               w w                   P                               L               Xx w                '  P                                L               x  x         #    (     P                               L               x pw                )  P  &                             L               xx x                   P         *                      L               x \x                c   P  	                             L               0x $x                K   P  )                             L               w x                  P         j                      L               @x x                   P  ]                             L               `x ty         j          P                               L               y tx         V       '   P  ,       p                      L               Xy x         5       !   P  +       
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       ]   P  V       "                      L               (T XU         0         P  }                             L               T 5                   P  )       E                      L               | T                  P  -                             L               T T         `          P                               L               U          _       9   P                               L               |U `T         G       5   P                               L               U 0T         U          P  2                             L               TU T         *          P          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6 T         '          P  [       ;                      L               T lU         T         P  B       Z                      L               PU U         K       E   P  C       :                      L               ,U U                  P         |                      L                         G           P  S       F                      L               ) LU         b       S  P                               L               U D         c       3   P  ?       N                      L               U T         Y         P         r                      L               dU x6                   P                               L               6 <F         O       _  P  y                             L               <U 5                   P  M                             L               L6 4             %      P                               L                6 p6                q   P  ~                             L               6 5         t       ;  P  ^       a                      L                xU         |          P                               L                                  P                               L               6                 C   P         \                      L                6                G  P         {                      L               $6 6                   P  x                             L               6 5                9  P                                L               6 8                   P  d                             L               6 U                   P  o                             L               l 5                G   P                               L               6 \6                %  P  s       8                      L               t6                    P                               L                6                  P                               L                 6                +   P                                 L                d6         =        Q   P                               L                                    P          w                      L               6          q        K  P                               L                |6                -   P                               L               h6 6         }v           P                               L                                	        !      s     A   A    K  C     o   G         1      y         c  Y        ;  R     _         9          )        O   a        ;     w   7                        u       +  d       '     Y              ?  a   1  Q  {                Q   c            [      m   K  9    /           v  #  `  u       n       K  +                      0    3     E   u        ]  ?   '    	  9      )   e      }   q      {                *  H        L     g   A       3           i      T  5   p  "     A  j  +  .  }          i      #   ]       /  N  %                        E        3  q  7    W   =                e    4    K             S       I       -   U    /  G                   z  o    c  #          k     =        q      {  }    /    U      O  I   S  E  +  s  M    g       \       e   V  Q  m          J  =     '        %  [    w    J  !  y  ^  ]       l      <  
  )         S         !                                    >    '      ;  1    6  i     o  P    M  ;               f  C  %     ,  _  g                  y  U  5  B      ?  t        W  a    7          -  %          5      O  Y  7  x  9  2  s  k  5  &    b        (  -               F      	  :  !      h  M   @    ~            _    X  Q                     3  r        ?  $        m     G          =  8            [        W    -  U        D  O  C  1      Z    |      I    C                             I           W                      )                        M                       	    	  	  	    	    	    	  S  	  	  		  
	  	    	    	    	  w  	  	  	  	  	  	  	  	  	  	  	  k  	  	  	  G     
                                              (   *   ,   	  .       "   $   &   8   :   <   >   0   2   4   6   H   J   L   N   @   B   D   F   X   Z   \   ^   P   R   T   V   h   j   l   n   `   b   d   f   	  x   z   |   ~   p   r   t   v                                                                                          	                                                                                                             
  	                               (  *  ,  .     "  $  &  8  :  <  >  0  2  4  6  H   	  L  N  @  B  D  E  F  X  Z  \  ^  P  R  T  V  h  j  l  n  `  b  d  f  x  z  |  ~  p  r  t  v                                                                                                                                        
                               (  *  ,  .     "  #  $  &  8  :  <  >  0  2  4  6  H  J  L  N  @  B  D  F  !	  "	  #	  $	  %	  &	  '	  (	  )	  *	  +	  ,	  -	  .	  /	  0	          Pr R               v           (c       *xS             ^ !   '	       l_                2            \R w               	           `6                           T                 w (             0             T          3              2        0F             t A   '	      	@		    $ }      DT g            ^ )   '	       			    d        `w             P[    <'	    K  	 
	4U       pq W            0v    8'	   R   	`
	    hH $     t O        |       <        ^ :     H B               l[ u        
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                       L                @                 R   P  )        A                       L               X          C           P  x        G                       L                                    P                                 L                0         n           P          j        J                       L               x          {        .                       L                         b        Z   P  <                               L                         K        \   P  Y        "                       L               , d         T        ^   P  Z        ~                       L               P h                 `   P          2                       L                                  b   P  S        0                       L               H L         ;        d   P                                 L                         -           P                                 L                         M           P  ^                               L               4 x                    P          h                       L               d $                    P  \                               L                p                    P  "        w                       L               l                     P  }                               L                         H           P                                 L                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      @  X        Z   T  ԧ         ( h         b       |  d        h                         t         u       ( y     L                                                   ԩ                  0         (	    D           X             l                            `                                  4                            !    ˸                  P            x    @              P          `          p                              0                                                                                                      p    0             @         P         `             p                                                                             t                                4                  0         @     |    P             `         p                                                                                                   `                           0     x    @             P         0 `     | @   p                                       }       ~                                                                                           0           @           P             `           p                                                                                                                                              0           @             P           `           p                                                                                                                                              0                          $            D 3                        $     c             d     0        e                                                 L               l @         K        &  P                                 L               ,                  (  P  N        i                       L               \ 8         W        *  P                                 L               \                  +  P  s                               L               x                  ,  P          l                       L                                 .  P  g                               L               0          \        0  P          J                       L               p          c        2  P          u                       L                \         {        4  P  _                               L                |                 6  P          m                       L                T                 8  P  z                               L               s                  :  P                                 L                x                 <  P                                 L                L         w        >  P                                 L                         	        @  P                                 L               $                  B  P          b                       L                                  D  P                                 L                         f        F  P                                 L                         j        H  P                                 L                                 J  P                                 L                <         8        L  P  n                               L                                 N  P                                 L               $ l         I             I                 {'                    I X         P                                                                                                                                                                                                                                                                                                                                     ~I                    I                I                I                    I                    '                    I f   G   g   i   k   l   o   u   w   {   }                                          !   "   #   $   %   (   *   ,   -   .   0   2   3   4   5   6   8   9   :   <   >   @   A   B   C   D   E   F      H   I   J   K   N   O   P   Q   R   S   T   U   V   W   X   Y   Z   [   \   ]   ^   _   `   a   b   c   d   e                             
                                 I                 I 
                   	<n	]I                 VI                    II                FI 
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                 	F                F                 F                h	F                F                F                 I                    I 
                   %     I                    I                
I                 F                F                F                    F                G                    G                G                    H                G                vI X         P                                               8&     % % %                                                                     % D%                 h% 8%                                                     p% %                                             t% X%                                                     I X         P                                               D     % %                                                                         % %                 % %                                                         %                                             t$ %                                                     I X         P                                           $%                                                                                                                                                                                                      %                                                                                 $& I 
                  c'    P               I                I                 I X         P                                                                                                                                                                                                                                                                                                                                       `K  gI                 QI                    AI 
                   l%     NI                SI                \I                 tI                 PI                   YI 
                       qI                 xI                    ZI                I                 I                    I                   H                 G                    F                F                F                    F             F                    F                    F             F                    F                6I X         P                                                                                                        @%                                         ,& $                                                                                                                                         $ $                             I X         P                                                   L&                                                                                                                         & @& & &          & &         %         % &                                                      & %             % %             y	5I                    -I                *I                /I                    'I                $I                )I                 I X         P                                                                                                                                                                                                                D                                                                                                                     >I                ?I                    +I                 %I                 4I                 I                LI                            < T             t  U    tt        Ll V    Dx         W     L        P             Q    I          R              S  	  1         \    (_        X  ]    xl         ^            8 _            D X    ] 4       @  Y    ] 6          Z    Ԧ D        [     g       x e    ^         f    @        , g    q d       h    0_ ?        `    |        x a     l         b             d d  "   ^        m  $            n  &  \        ( o  	  n         p  (  _ /       H i  *  `        , j  ,  lH ,        k  -  4        X l  /  \ ~        u  2  |H         v  5           w  8  0 x       H x  :  |          q  =  Lv        r  >  4          s  ?  4S        t  @  ^ (        }  C   R        ~  D  y 8         F  4w          G  m         y  I  Ħ         z  L  P X       l {  O  ,v        ( |  R  G        h   U   H       L   X  4 S            w       H   Z  ^           \  [           _  <           b   Z       p   d          (   f          L   h  "        |   k  x^ 8       8   m  H .          o  8           p             r             t  P           v  D           x   s          z  H           |  h           }  XP        8   ~               (y @      p     ` P       P     $ Y            @         T     ,              m             G 0       l     v        $     ^ *       D     ħ `       4     Щ             8 V            <w       8     d n       L     r a           ] &            \ =            G '       (     p r            \        T      p       `     ^        ,      a       t     p_ +            w        4     ^ 7            ] "            PH #            x 5                       	  v       \     v        ,   	  S       (     Ĩ w            Tw       T     R          	              8        \     4        h     8 F                    k     w            h             H\                           x .           $y A           z V                        T            <^ 2            0y F            j       $                 ܨ q       t                  >        8     ,\             \ i       H     H 3          	  P\             |v             \        d   	  v              ]          	  (            u        8   0	  <R       d   	  Lv           	   /      P     Z             ȧ f       ,   	  | m       t      W   $	       x )  %	       h c   &	       Z    '	  `   	  [        `     ^ %   !	  4     ] ;   "	       6   #	       u             Pr R      t      v       H     (c          	  xS   (	  @       ^ !       0       l_               2               \R w              	              `6                     p       T                   	  w (                     0                            T                3             2         t       0F              t A       4              D       $ }       |        DT g       	      ^ )        
              T       d               `w       L       P[                K             4U       `       pq W             0v        x       R                e                ?             Dr q              K              Z               py 7      t       5              H               < U              x ?      @       X6              Xw               -                      "             t #      S        $      4 %       %                    x  1      4        {      $       $ =               !       *       )      L +              ,       E        -              \ &      8T       t '      X         (      P^ -       D )               2      q Y      L 3       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  8U       dy D    U       8v      m        H B         	  `              \c       [      P        |x "    q i    b       `R     xT     \r n      y B    (x 1  	  [    	  y J      y <  !  Z        1    #  \T       w #  %  R       y N  '  S       r 4  )  X[        v   +  q f    b       \    .  v        @ t   0  Ȧ I   1  `S       m    3  x    4  r s      7 T  6  tv    7  \U   	  ԧ \   9  S       8r Q  ;  Ly 2  <  5     y L    h   
	  R       |]    A  r t  B  6   	  pU     v 
  E  R     1      m    H  6       x   J   k   K  [        q Z  M  v    N   c       q X  P  \w   Q  G        Hw 	  S  D\    T  06       w   V  r |  W  T   	  XR   Y  D6     w $  [   w       Hx ,  ]  hx +  ^  S       Ч d   `  r }  a  TR     `    c  G <   	  2    e  xq b    q h  g  S       y U  i  x    j  xR     Px /  l  $w      h   n  h      [    	  v    q  T   -	  v   s  r x      ( y   u   b       w &  w  b       x *  y  H        v    {  H6          dS       b j    r m    Tr ^    r       xw     T       m       F       @U     l6             _ 1             <T       Xc p    S       2      4R   	  Pv      T     w      r \  ,	  x :    r u      y 0    <]      q l  /	  PT     ,     T              T     v      R        >     1      |R     v    	  Ԩ      U       L z     |1    	   N   	  l        w     [        ly >            ] @     r y      y P    b        r `    LR z      dv      m        T       PS               [        P6       ]        @R       lv        <        ^ :       R       T       tT       Xq ]              0U       l[ u              @r k       
       v       tR       x 6      b o      |S       v       m        ^        ԩ        lq M       o       (U       hc              <x '      U       DS   *	  6     6                          `                   P        <       T            0   	   	       
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               4                                          d                 ~                    ]
                 W                q                E              c                  U 
                   L     d                     
                    ?                  X                b                                      
                   05                      [                 e                                                                             6                                                                         ;                  ;                  =                  b                 ޢ                                                                               ̰                 8                                                                                    d                                      0                 `                                                  D                E X         P        P                               @ <              | $ X l                                                 | T                               t x p     , D             L 8                         @            <                 8j {                                                                     `  
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            |     z`                 B                                 C                                                                   W              X                     H                  K                     j                                   -                  -                                 .                ,                    (                    c                 @                    E                                l                 A                      X         P        x l:     <                 (     . 0                  L H       l , l L           , `                 :           . :                 :      / @     : t:                   4 .             T
 5 :   t)         :       4 @> e                 3                    y                                    ϳ                                      OM                      
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                                             )E                    %E                &E                E 
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                H     ~                 %                                   ~                  B                 .o              Y                     O                  X                                                       y                                    d                 : U                 Z                                                                          E                                          `                                  v  
                    ^                                                        e                  Q                 ͜                    ~              /_                                                         O                                                                                                                          |D                     H                    '                     %                    ; 
                    u H                    G  X         P   `S           | g  W     4 <f 8             
   4 $ D, b   T     L 05     ) \ <    x 4 0 l p           \        Ԅ T     t   L Pe 8 <           `                        l T X       ֡                                       NR                                    L                                                                     w                 
                                                  N             h                     !                                                  D                    D                D                D                                  
                   h     /e                     DE             ; ^
                E                    E                E                    YE                 rE                x E X         P   D%       `                             4 H              l h  X         L \                                                                                                                          t          , h `     H 0F D                    D                D                 P                                     E                zE                E                    	E                 E                 E                8i _E X         P   T&       x                                       D         $ ( 0        P 0     (          l                 $                                                                          d     P                 (                   W                                       ʟ                     #                                                     Ҏ                                                         u                  ~                     Rb                                                                                                               Zl                                                        h                                                           I                  z                                                                                            o                                   ;                                                          u                                                                      S                LM                                                                              D                 D                    8E                 p                     ;                                  f                                      U                                 D                E X         P        L                                              T      ( 0         D           T                  p          @                          \     8 x             0       D                                    B                                                    %                                       
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                                                  #c                                    X              Y                    c                                  R                                                 @X                                   w  
               (                      <                     #                                                                           х                 Δ                                   Re                                  Ye                                   J                     ~                  =W                 A                T                     ߟ                                                         Ǻ                  ß                                    f                     o                  ~                                      g                 e                     h[                                                           &                  le                 {                  t                                       D                 F                 c                                      M                                                    @v                 5                                  ]                       X         P   \/     x) f     4              $      :                 :  : p 8 T .      T  (  h         : : p:             / 4         P                       4                4          <              4  ) 4 4 H          5  ,      
 u                                      \                 ^                                  jM                  He                     `                 7                 f                                       T                                      a                  Ъ                  А                  ğ                     V                 I                  }                     G                  k                                       q                 Z                 ň                 w                                       oe                                      q                                  Y                     c                                       H                                                                                X                                       ٪                     Sb                 ~                 ~                                                           q                     qq                    f                  z                 u                     0                 q                               ?                     `q                     q                                       z                  ws                  r~                                     -M                                                          X         P                                                                                                                                                                                                                                                                                                                                                      K                                   ذ                    n                     l                                   ʰ                                      e                  e                      X         P   `     4 xW     |D             8, 4      4     4         4 4 ē f  h. $      p F / p l
          P L     ) (G 
 |         5 )                 H      4     T, +              H     ` @,               (,             , 0     ,                   Dq                                                        y                  H                                                                              K                  b                 b                                                                             ֟                  	                     ڡ                                   ~q                     Z                                   nq                                         q                     ߰                  V                  Yq                 d                    q                  T                                                       8                     9b                  cb                                          p                                      ,~                                                                          TY                     >                     bt                     V                 T                 D                     ׏                  Y                  Y                                      h kS  
                03 p   X         P                                                             p H g                                                                                                                                                   H \D                                         `                <                                                                               ū                                          Se                                       =                     B                 t                 S  X         P   4      ,F  i                             | E         Ti       `X    Tf Е     t   x  d         <F                            LE W                      E      ̲ W             ,E DF      F             HE o  Ȋ l 8h         @ X      Գ :  X         P        p5 P     L,             X, d     T      0,         l T- , l   4     4   5      ;           4 4 4 x , 8         ,, ,                 p           +          `          4 0              d ` 
 H \         <  T     T `e                  !  X         P                                                  t                         \ 4                                                                                                                                                                                                          h                                 p                    R                                      
                           ˍ                 S                 S                  S                                                        ~                     7                                    
               N     C                     ~                                  S                     z                                       |  X         P                                                                            T                                                                                                                                                                                                                                                      k                 V                  ~                     Y                 M                 S                     i                 T                 .[                 d[                 R                  L                     d                  \                  6                 ĺ                                   ~              l l  
                                                L                                  e                                       L  
                                     ˭                                      K                                   }                 #                     ̎                 c                     n                 e                 y                                                            ?                  _                                       c                                   @~                                       b                                   W                                      L                                                    e                     X                                      cq                                   t ґ                                  ۝                     E                  <                                                    s~                 ~                     OR  
                                     \                                                    i                 b                                                                       ~  
                 U T                                      Kb                     R                 Ƃ                  J                                      :                               Д                                      w                 ?                                    K                                   "                      }                 Ho  X         P   R      @      H          ļ T H               l 8     ` |     \ T        h T                h  H      P  | \  p d|           X d  X HS     L{  x %     T       \,       }                     Qo                                      q                 3q                  V                     Sq                     \                                                                                                                                                     9                     h                 >                 $                  Z                                      1                  oo                 q                     q                 Ue                                       q                                                                                                    -~                 F                                          e              W p                 ;                     u                   
                   8/ ł                 .b                    ~                                                    #o                    Ȱ                    {~                 ~              Yb                 Bo                    c`                                   W                  ~                                         հ                                                     -e  
                   D     ~                                       n                 ?                  l                  X                     ١                                       [                 ib                 }  
                   <I     U                                                                     G                  b                    
                x                          \                  I                     #                  A                                                                              ;                                       .                     c                 w                                       u                  k                                          ª                                   	                q  
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 0           f ,             |Q 
 4                      `
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     4  4      t     t 
 f   Xh TM                     v                  S                                                        v                  O              	l                    ]                                      H                   
                                   H~                                       u                     u                  ݩ                     ν                                   
                                                                                                                   q                  l                     Pq                                   .                 |                                     0                 ~                                                                    ~              Eq                     ֪                 q                 q                     ޵                  b                 ǆ                 ~                 a                  !                 b                                                                                      /              v                                       q                                   W                 Յ                    e                  ۽                 N~                  X                     m X         P   (     4      X 
        p  Ԍ   (         0     q X \H       4     o h | L X     P
 أ 
         
      H X 
       4 \ <                    ܢ @ L p       D |       8      XW  ht h  Z                 b                                                                         ~                  b                                                    ~                                                                           ]e                                                    e                 U                                     JI                 u                     ^                 ߡ                 +                 @X                                   q                                      Ѩ                 w                     ~                                                     a  X         P   @S     b (        x     D P  , H          `   8 \  0      h (        d       d   d         , 0        l     $ \ X  d x            $$ l  4      8  t      (     $ 4 D |      u                 1                     pb                  ~                     I~  
            D     q                                                       ׵                  'o                 ~                 Lo                     l                    G                 Y                 
                 l  
                       O                 Wq                                      .                                         
            +     mq                                  Z                                      Rq                  NM  X         P   @&	                                                                         (                                                                                                                                                                                                                                                  G                                                           X                     ̪                                    Q                                                           
                        2                                                                             |q                  0o                     Ӫ                     Zo                                   &~  
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                  H     T~                  f                  (~                     Nq                  6                 ]o                 e                     ot                                  *a                                                          X         P   5     <        pW        d  
  < h         l t p d' <5  5       < \     Ȍ 4 $   l0   x
    g         l ,      / T      d/ / @0    X0 4g             W  \ `	  1     8/   P.     X      l& ( P X                                         H                     \                  >  
                8     xq                 ~                                                       Q                  i                 y                  d                                   Г                  ~                  ʹ                                   a                                          -                                     b  
                    R  
                ! pu g                                    ~                     u  
                       ݛ                 ?                                    Ke                  ˰                  U                  f                                      y                                       u                                  %                  ׺                  T                                                                             ru                  7                                                            ]                                                        `                 # 4                                  Y                                                                             +                  #              ӊ                     tU                                                        D                     f                  i                     4                    `                 k                   X         P   9	     x ,                             С p               p< <                           l                                                                                       t                               4                                         t               |p                              | *                                ?                                      ~                                  q                     N                                                   K                                       թ                                       «                 $                 e                  ^                                          SS                  .                                      '                  g                  ͩ                  F                     `                                                                                                                              V                                                                           1                                                   ^                                                        d                                          c                  ]                                          s                     U                    
                0                          te                 X         P         D"      ~             D ث     N      D         " 0"   !  8     p a      | d          |      {            8| I                 p     z       (                    (             0;   d{                  8     u                                   -                  h                     @e               <              | q                     ܛ                 L                 :                     k                     w                     x                     v                  <                     ;                  e[                  c                 k                     W                 u               W                                                                                           Y                                                        'M                 F                     7                                          b                                                   R                                  y                     S                                  Xe                                     ^L                 GL                L                    L                    L                    L                L                L                    l  
                   ԭ  $                  l              p V  
                                       c                                  =[                                   Y                     T  X         P   <     |      " a       4    d D                 ( @S           x t X 8i  C ԗ X   `           `     <      t 8  (  D          L   d H      h  T ܻ           |  , 0 a '                 y                                                    lr                 ae                  e                   
                    ]                  c                                                           l                 K                 O  
                     8                 p                                       i                 ^                  'e                  g                  L                     &                     ?                     	                  k                                       K                 m                 B                  ֛                  v                                                           7                                                                                                  w                 !                 w                 k                                          T                 )                 T                  t                     V                 y                  m[                 v                  -                  r                                                            z                                                                                              ʵ                  p                 w                  	                 Ie  
                P d              4 y                 ` q                                                                                            d                     q                                   ̛                                                        Y  
               H      x                     p                  \S                                          o                                                         [                                                    õ                 s                  =e                     2                 gS                                   y                                                        l                  p                     d                 y                 }                                                        |e  X         P   ]     X {                              h o              M    : ؄         X  H' (                            :         H                  d       C     , :              \      PR             o  o 8           M  p\     $ < װ                  y                     j                                         
                     ue                  y                 Qe                                                              X         P        ̄         8        ,  X h          ` d  l  x   0           T T  (% 0 x  ̋   t          +     H        H   l              `       <              D       X         P   R     p e     (- |+  X"      n P                 آ  @     L h     |  X  ( | @  g    d!         $      ` pu ! P"      a ha # ! l       "     T " `  !     "  `      ؖ     $" | X| p tM     K                  k                                                            5                     Տ                     '                     g              :                  C                    
                           h                  L                                                        q                 z                                   y                                                        5                                                                            Ѕ                                   q                 -                  \  
                  P^	ʸӞ                                    K                     a  X         P                                                                                                                                                                                                                                                                                                                                        V                 s                     (                                          X                                                                          Y                                      q              @ u                 l                                      Ο                     I                    I                    G                G                    F                F 
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                        E                E                E                E                    E                    kF                    bF                 %F              F                 'F                E                E 
                        0F                6F                 nF                _F                 OF                F                 F                    F                 F                    E                 F                    F                 	I X         P                              $                                         h$ $                 % T%     @$ #                                                                         ($ $                                                              $ $      $                                                        F X         P   H                    T                 #                                                                                                                                                                                                                                                                                      	F                    F                 fF                   rF                    vF 
                        yF                 VF                    ]F                YF                \F                I X         P                              H$                                         l $                 $ $     <$ #         #                                                              4H                                                               `                                                      #	<F                F                E                E                 E                    E                 E                F                E                    E                 E                    F X         P   (    x | H                                                    0 (                         8 ,                                                                                                                                                                                               t                                     UK                 +e                                                                    d                                                                            Z                                                       .c                 :                =                 d                                                    Q  
                d'     @E 
                 3E                    LE              AE                 2E                -E                +E                ,E                    E                 'E                    @                                     wq                    y`                                                                                                             2c                                                                    a                                                                   3M                                                                                           X-	D                D                 D                   D                 D                D                 D                    D                 D                D 
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                pS '                                   #b  
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                       @<	@F X         P          P  ,                              D               $                         <                                                                                                                                                        l                          E                                                   P                M                  V                 I                	                                                        fM                                      O                                 9                    d                 c                 G                 g
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                                                                   _                    
               m	E	Q                                     5                %                                                       0                z                                                                      
            q p,                         vE                 |E                    XE                   X         P   `S            0  w     |   ? 0          ȶ W  (   | ,      t        $ D   h p            N \     (   c        HG  B            Ě    <I     W  (      H     D                                           8                                  qt  
                   x                      g                                      q                  f                                      U                                                           f                 M                 }                  D                 *                     !                                                       '                                                                    `  
                                                                            KE                E                 E                     E                    .E                 EE                 JE                    ~E                 E                    G X         P   	                        #             X     < D            (                 ,                                                                                                                     0 x t                                         ` h     G X         P          D$                                                                     $ $                                                                                                                                                                                                             $                                F                    8F                 E                    "F                    E                E                E                E                 E                    E                   E                 F                    F                    {F                    hF                    KF                 ;F                 GF                    QF                    FF                 3F                ` 1F                 F X         P          %                                                                                                                                                                                                                                                                            ,                               U	F                 pF                    -F                F                7F                 E                    E                 E                    E                 E                E                 E                    jF                F                    !F                $F                    MF                 E                 iE 
                           E                    :F                   F                    F                    F                    =F                PF                    RF                 IF                    CF                 AF                    F                 BF                F X         P                           X                 x 8                                                                                                                 t     # h # $         X$ #         $       <                                                     P $                               F                dF                 cF                    mF                 XF                    JF                 DF                ?F                    F                 F                    F                 F X         P          &                                                                                                                                                                                                                                                                                                 b                                                       q                 R                     a                     (                  1o                     E                cE                    E                 #E                 D                D                D                    D                 D                D                    D                 E                .F                 F                 NF                 
F                E                    E                    E                 E                    E                 	F                F                    [F                    E                    ;E                uE                 tE                    oE                    QE 
                PT `T E                E                E                E                E                 E                    E                E                 E                    E                 E                    E                 E                    E                 E                #F                    E                }E                    E 
                          E 
                S     E             ˸E                    E                 E                    F                 +F                    F                F                F                >F                    E                E                    F                    F                F                WF                gF                F                    E                E 
                        F                 F                F                E                E                F X         P                                                                       D                          h 4                                                                                                                                                                         p t         L     H                             f`                                      D                E                                                       D                 D                E                 E                    GE                    ؟                                                       
E                    e                 6                                      g                 ` 
               Xl		ʸE                    sE                 E                h E                 E                 D                 E 
                   (     E                 *E                    !E                    ^E                 E 
                     wE                    E                $ E                RE                                  =M                 (                                                    U~                                      y                                                                         Q                 R                                  A                                                                                                                                                     D                6                      f                                       ?                 2                    `                  p
                +                    /                    `                  D                D                 E                D                D 
               T     9E                 E                    D                 D                    yE                eE                xE                    pE                 jE                 gE                F X         P                              8$ p            |                                   @          $ d @ D                  8                         $                                                                                                   \    F                 xF                ^F                 F                    4F                    ,F                    )F                    *F                   &F                   9F                 F                    	G             ( F 
            \ L ˸F                                  q                    X         P   P      da     0a `! X H     H" m P \a )            8 + 0 $ h       h)     ,  ,  , <% O `, ` Da 4s  |         0| |       D        po 0          z          4 t L |       C <Z      H      o    : 	                                      :                 n                                      Q                  me                  )                     lq                 jq                                    ʅ                     ͑                                   ~                     o                     ~                  q                                      ,                   X         P            4     ī h 4\          ( ,6              <  f h \t     w       H `  t    L   l         @  8 Ї    P     d L h     $         ԫ  D Ȳ t 8      ܫ  4     P      8                             q                                                                           ~                    oY                 J                  J  
                   +     (                  lt                     Q                     u                    
                 `R                                    v                     P                 Y                 ɨ                     Bk                     8                                       l[                  W                     Y                                       M                 0 Y                     I[                 d                  TS  X         P   	    P T                                                      \4                         f (                                                                                                                                                                         df          x     8               X         P   	    < H <                             h          h     D  ( E t       Г T $X $                 ġ d                 8          T Th                      X      T ,             s h                           7          T         0 ء @     f     z  X         P   @	     ܔ     M                         M H:         @C     T?           $ X   a  `          :                 h `         : X                 tL     p M     ܅ g             M      ԕ               T hM (  D ;         n ̔ T     ,                                               O                                      i                  Y                  d                     ԛ                  Y                                      k                     ˨                                          Q                                                      kr                     7[                                                         [                 {                                  y                 y                     v                  W                 y                                   ώ                 N                     $                  ee                     ;                                       7                  e                       
                                                          "                                                                                           ]                  m                     a                                       y                 J                 r                                                     PT                                                             ެ  
                 @Q n                     s              <= 3e                     !                                  Ұ                                      p                                  {                                  y                 y                                       y                                       y                  %  X         P   	     }     4             H      |      ,|             H  T     (  a     ,          ܲ @ D  x X  b         8 !                 <"     ! (~     l"          ̮     |      ,             o    P L          ~ $ |          %                  !l  X         P                                                                                                                                                                                                                             i                                                                                                                                       V                     T                  Y                  T                                      ?                 c  
                                                           z                     e                    
               E |     y                     }                                                            L                     S                     j                 o                                       Щ                                                                                   
                m                          }                 y                 t \                 v                  ΐ                     /                     O                  mS                     }y  
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                        c  X         P   	    ~  \                                       `     D  ,p ; , dt :     5               P ,                 T}           f                 4     F ԡ                     \T      P              ̦   E .          0E pF     `     y                     `                                                                             -                                                                                                               H                  k                     \                 \                                          g                                [                                         
               t      6  X         P   	      \ dX                              Xh         $g     0N `i h   E E     M  4~ A                  <}                 Xo ؝         0 pE                     E 8C      W X                                       h T  x  ܠ         hh D      T     d  X         P   	    x                               L          h     p Ȯ  ĵ     < $h       ,                                           е                                     |g `         ܴ              X Ԣ                                         P P               \.             Q                     p                  iS                  k                  S                 `              HM                    P                 T                 x                     W                                                                             =                 y  
                xW	ʸ                 ƫ                                       \                     `                                                            Ԩ                                                                                                                 ͫ                                    r                     ߐ  X         P             P                              $          g     L  x    ̡     A                                              h         4 (                      g Ģ     h n             T                                          \g L         x < =     Э     T              T                 Y                 T                 h  
               f h	̌                  `M                     1Q                     u                     [S                   X         P          <                                                                                                                                                                                                                                                                               t  g                                 x  X         P           $                                                                                                                                                                                                                                                                                                                                                                                                          S  
                                                           Y                                      k                 YM                                    V                 V                                  e                 1l                 q              p< `                 at                                         X         P           W                               4 H         =     X = 0 <= @  l       l                                           =         X 0                      خ @     l |                                                       x          h                  m                     3                  ~                 V                     c                  JM                     T                 2                 z                 $                                      U  X         P                                                $ 4&                         4o 8                          T                                                                                                                                                                         @ f         h     \             @                    
                     T                                       k                                                            [                  B                    Y                  z                                      Y                  z                 h                       
                       D                     M                     @                     k                                      0S w  
                                      a                     V                 w                     v                  M                                      |                     BZ                                    ce                     Y  
                    M                 ͛                 U                   X         P                                           0              , 0o  tg                         o m                                                                                                pM             Ȣ f                                         P |M                           p  X         P                                                                                                                                                                                                                                                                                                                                        {  X         P             X                              @         8     ` (g 0L =            0= = Xr                                         = g           (                     ȵ 4      t              T                                           g                                            w                    T                                                       T                 T                                   h                                                        ~y                                                                              ɫ  X         P             D=                              @N              |<   PT    4     \  L                                          ̝          < M                      g l=      ,              = ,                                         X> Pg         =          W     S                  L X         P   '                                                                                                                                                     3                                                                                                                                                                          L X         P                                                                                                                                                            3                                                                                                                                                                           X         P                                                    E R U                                                                     *                   %                             E 0                 ~                                               `q                                          L/     K 
                P                       +L                8 .L             9 /L                                      r                  (L                                          'L                                      #L X         P                                               0     E 0 a                                                                     p 9                    G                                                     ,a 0                                             0 0                                                     L                    LL                 tL                 L                L                    L                L                L                 L                L                    L                1L X         P                                               4     0 P                                                                         8 p                 0 0                                                     0 0                                             0 0                                                     `L                    DL                OL                 L                L                    L                   L 
                       L                L                    +  X         P                                               4     E 0 x                                                                     N P                 L X&                             X 8                 `                                        ,V P&                                          G                          ?L X         P                                               4                                                                                                                                                                                                                                                                                         AL X         P                                                     $ <E                                                                                                                                                                                                                                                                             qL 
                  P P \L                 IL                    JL                    BL                CL                L                   L 
                       HL                   X         P                                               t     P q &                                                                     j ԭ                 H T                                                0                                             0 0                                                     iL X         P                                                           0                                                                                                                                                                                                                                                                             <L X         P                                                   E                                                                                                                         0 1                 |1 1                                                                                                                             L X         P                                                                                                    2                                                                                                                                                                                                                                     L                 L                    L                    M                #M 
                       
M                    M                    L                   M                n                  S              m K                  8M  
                f     Y                 m                 F                  d                     Y                                                          k                 ;                     d                     ,                                                      f                 @L                -L                   Y  X         P   	                                 N                                                             q Ȯ                                         $g                                                                                                                                          \E dE                             7  X         P   	                                $                                                                                                                                                                                                                                                                                                   X         P   	                                    $m                                                                                                                                                                                                                                                                                             T  X         P                           P5                 4p $                                                                                                                         5 d5 h Z         Z          E İ      t5                                                                   (5 R                 #M  X         P                           }                                                                                                                                                                                                                                                                                                               X         P                                   H                                                                                                                                                                                                                                                                                               Y                  w  X         P                               hZ                                                                                                                                                                                                                                                                                                         hL                 wL X         P                                                                1                                                                                                                                                                                                                                                                         L                L                L                L                    L                    L                    L 
               3         L                L                                                                         L 
               zo;o                     K                 =L                 )L 
                       f                   X         P                                              XE                                                                                                                      H (         Z          DS R      Z                                                     p               8S                 h                                                         S                     X                 ԭ x                     ?                  _                  +                        
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  X         P                                                                                          m H     ^ @                                                                         ̯                                                              LD lE                                                                                   0L                 RL                 PL                    gL                    vL                    zL                }L                ~L                    {L                   L                yL                    Ii                     i                                   %L                 &L                     L                n                                     ܂                  `                                          _L                    L                    L                L                L                    M                M                    L                L                   M                4 	M                 dL                    QL                    L                L                    L                    L 
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                       L                L                    L                    4L 
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2 $2                                                                                                                     L X         P                                                                               <2                                                                                                                                                                                                                                                         L X         P                                                                               2                                                                                                             ,2 2                                                                                                                                     mL X         P                                                                                                                                                                            0 1 1 <1         D1 1                     1 1                                                                         1 1                 L X         P                                                                                               l2                                                                                                                                                                                                                                         L X         P                                                                                                       2                                                                                                                                                                                                                                 EL X         P                                                   \                                                                                                                          1 $1 (1 01         81 H1         L1 X1     1 `1                                                     h1 d1             x1 1                 ML X         P                                                       0                                                                                                                                                                                                                                                                                 cL X         P                                                   1                                                                                                                         | t1 l1 P1         @1 ,1                     1 1                                                     1 1             1 1                 L X         P                                                                                                               2                                                                                                                                                                                                                         L X         P                                                                                                                   2                                                                                                                                                                                                                     L                M                    M                    M                    $M                 %M                 M                    M                    L X         P                                                                                                                       2                                                                                                                                                                                         2                     L X         P                                                                                                                       2                                                                                                                                                                                                                 L X         P                                                                                                   T2                                                             2 2                                                                                                                                                                 L X         P                                                                                                           2                                                                                                                                                                                                                             L X         P                                                                               82                 (2 2     d2 \2                                                                         L2 @2                                                                                                                                     L X         P                                                                                   42                                                                                                                                                                                                                                                     L X         P                                                                                       H2                                                                                                                                                                                                                                                 L X         P                                                                                           2                                                                                                                                                                                                                                             L X         P                                                                               2                 02 2                                                                                     t2 |2                                                                                                                                     |L X         P                                                                               2                 P2 X2     D2 `2    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M X         P                                                                                                                                                                                                                                       04                                                                         4 4                 (M X         P                                                                                                                                                                                                                                                       4                                                                                 1M X         P                                                                                                                                                                                                                                                           4                                                                             3M X         P                                                                                                                                                                                                                                                               4                                                                         5M X         P                                                                                                                                                                                                                                                                   4                                                                     7M X         P                                                                                                                                                                                                                                                                       4                                                                 9M X         P                                                                                                                                                                                                                                                                           4                                                             ;M X         P                                                                                                                                                                                                                                                                               4                                                         =M X         P                                                                                                                                                                                                                                                                                   4                                                     ?M X         P                                                                                                                                                                                                                                                                                       4                                                 AM X         P                                                                                                                                                                                                                                                                                            5                                             CM X         P                                                                                                                                                                                                                                                                                               5                                         EM X         P                                                                                                                                                                                                                                                                                                   5                                     GM X         P                                                                                                                                                                                                                                                                                                       5                                 IM X         P                                                                                                                           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5                             JM                    KM X         P                                                                                                                                                                                                                                                                                                               (5                         LM                    MM X         P                                                                                                                                                                                                                                                                                                                   05                     NM                    >M X         P                                                                                                                                                                                                                                                                                                                       85                 PM                    QM X         P                                                                                                                                                                                                                                                                                                                           @5             RM                    SM X         P                                                                                                                                                                                                                                                                                                                               H5         TM                    UM X         P                                                                                                                                                                                                                                                                                                                                   P5     M                    @                                 <      L= 8=        T                         $     $     a a         '                      u   '     '       T          U 
                          ]                J                    =                 &                ?                     
                `     8                -                    Q                    $                                                        . 
                   `     %                                       )                                                        2                3                0                    >                ;                    1                 +                    5                                                        6                                     (                                                                                                                       
                   d`     9                   '                                                                <                                                                                                	                                 '                   *                                   #                                                                                                                                                                                                                                                                               
                (`     !                                                            '                                                                                                               
                                                                                                                                                                                                                                                       
               `_                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
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                  ^                                                                                                                                                                                                                                                         @                                                                        L                                                                                                                                                                                            V                             1                 Q                    9                2                   S                C                 I                   (                   '                    M                    A                                        ^                >                                 0                    3                    #                |^ /                E                    6                    .                T^                     <                    8                                        P 
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                :                    "                                                                            $                                                                                             ,                                    +                                    *                                   '                   !                    '                                                                                                                                      '                                                                                                                                                                          '                                                                                         	                                                                                                                                      4`                                  `                                 _ t                                _                                                                         r                 l                    ~                                    s                    D                V                 z                XQ                 n                T^ ^             |                Q u                v                Q Q                q                    y             xQ w                P ]                i                                     b                TP k                e                                     a                O R                    g                    d                Z                    G                    [                N f             S                                       `                xN \                _                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  p                                                                                                            {                 }                                                                         
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                _                 ^                 _                 _              x_              ^                                                                                                                                                              tQ                                                                                                                                                                                                        O                 8P                 $P                                               O                                 $O                                 O                 <O                                                                     N                                                               XM                                                     M                                  L                 M              L                                                                                                               $C                                                  C                                 $B                              8B                                  A              A                                                                                      @A                                                                                    A              x@              @                                                                             n                                        z                    {                    w                    }                    8                                        v                                        |                    x                    j                    g                    t                    f                    y                    S                                        V                    b                    ~                    Y                    _                    L                    h                    c                    q                    m                    :                    a                    i                    Q                    M                    [                    ^                                        k                    C                    K                    W                    \                    D                    P                    H                    U                    l                    X                    e                    /                    J                    o                    O                                        2                    '                    T                    7                    I                    R                    5                    ;                    B                    @                    A                    N                    <                    E                    9                    "                                         %                    $                    4                    3                    =                    `                    F                    ?                    6                    +                    &                    )                    G                                        >                    ,                                                            (                                                            #                                        1                                        !                                                                                                                                            -                    0                                                                                *                                                                                                    .                    A   <     = ,^ = TO = ^ > P = PP = _ X=  M = N = \N = M P> L = ,` = P = N =  N > O = N = = = M = DQ |> 0N > h^ = 5 = M X> LO =  ` > M = ^ > @P  > 4N (> _ > hP > <` d> D^ > l` $>     t> PQ p> ^ = _ > |_ H> M \> $^ > O @> M > ` > O 0> h_ T> 8N > O > HQ t=  _ > O > _ D> XP x> = > O > hM L> dO > dN 8> lM > _ `> P <> P 4> tO ,> N > TQ h> D` > ^ ? <_ > @_ > tN D? ^ ? L^ > ^ > N > ^ > O > N > N ? 4Q > ` > X^ >  ^ > D= > \` > \Q l> XQ  ? 8 ? ^ > ^ L? H^ $? ?  ? l^ ,? N > T^ P? PO h? _ 4? < ? `Q 0? Q @? ^ T? P ? Q ? 5 \? D_ `? P X? ^ x? O ? ^ ? 8` p?     <? LP t? (_ d? P > ` ? |O ? P (? P ? x^ ? Q |? N l? $Q ? xQ ? |P 8@ _ ? P ? _ ? P ? ? 8? @Q ? T= ?  P ? P ? ta @ P H? \P ? pP ? `P ? O @ HP ? tQ ? ` ? `  @ T_ ? TP ? L_ @     P     dP P O ` O 8P O O O $P 4P O O hQ O X_ ,P _ 0P ^ lO 4^  P O O O O T` N _ O O O _ O O HO ^ xO N N _ O 8O \O Q O ^ 4O ` O O $O _ (O N `O = N _ 0O DO  O ,O N pO O XO O N N     hO  O @O N <O N N O N t^ N N O P` pN ^ N N O ` XN N N \_ lN N N N `N TN xN ` M N $N ` hN N @N _ PN ^ M ` LN _ |N ^ M N  N N N M N ` (N H` N DN N M M M M M M M M p_ XM M <N xM M M M t` DM M M ` tM _ HN _ M N HM M M |M M M LM M M (M ,N pM M M M L  M `M L L L TM L <M PM $5 M _ dM L ,M ` M M 8M @M \M L L M $M L 0M L L L L L L t5 4M 5 L L L ` K <5 8 85 L     L  8 05  @C C 4  C d` C ,C M 4C B L C 5 L ,5 L 8C L B X5 PB 5 B B B |B L $C B  C <C (5 B B 0C (C C B B B B B B B hB C xB pB B dB 8 C B B B L B B @B tA B C B B \B B     B A B A `B B 8B DB B <B B 4B B  B (B A tB B hA ,B A A A XB HB  B B A LB A A A A @ 0B A B A A A A A A A LA B XA A A dA |A 0A A A A A @ A A DA 4A lA xA L@ A A ,A \A pA A @A  A TA A `A A @ (A A <A B @ @ PA @ $A HA @ @ A  A A 8A @ A @ @ @ @ @ @ @ @ A A @ @ @ @ @ A t@ @ @ 0@ D@ @ |@ x@ @ p@ @ @@ @ `@ l@ @ h@ ? d@ @ @ <@ H@ P@ @ X@ @ ? 4@ @ ? ? T@ @ ,@ ? $@  @ (@ \@ @ ? O P P P P O lP P DP P P P tP P P Q P P P Q P P P LQ P P ^ Q  Q P dQ Q Q P P 8Q P (Q lQ pQ <Q Q (^ ^ @^ Q ,Q ^ <] Q  ^ ^ 0^  R 8^ <^ ^ `^ d^ \^ 0Q ^ p^ H_ ^  Q |^ ^ ^ ^ ^ _ ^ ^ P^ ^ ^ ^ ^ ^ _ ^ _ _ 0_ ,_ ^ 4_  _ x_ 8_ _ P_ l_ _ $_ d_ _ `_ _ ^ t_ _ _ _ _ _  ` _ ` (` L X` _ _ ` $` _ _ ` 0` _ ` ` ` h` ` `` ` x` ` @` ` 4` L` p` ` ` ` ` ` |` Da ` ` (a 4a = TB d= 0= @= = $= lB B = = x=  > \= (= l= p= O P xP     '                      L                \         '       '       '       %      '       j                Q                : 
                                                                                                                                                                                                                                                                                                                      z                                                                                    ]                                                                                                                                                                                                                           ~                                                                                                                                                                                                  a                                     |                                 q                    `                                                     k                                  {                 f                y                                t                w                    u                 x                                     d                 r                n                 V                    c                    i                                  s                    p                 }                 m                g                ^             L                    Y                A                                    W                    J                    [                    \                    h                 I                P                 e' X         P                                                                                                                                                                                                                                                                                                                                      ˸S   G      H   F   I   E   J   D   K   C   L   B   M   A   N   @   O   ?   P   >   Q   =   R   <   S   ;   T   :   U   9   V   8   W   7   X   6   Y   Z   [   5   \   4   ]   3   ^   2   _   1   `   0   a   /   b   .   c   -   d   ,   e   +   f   *   g   1   h   )   i   .   j   (   k   ;   l      m   '   n   &   o   @   p   %   q   $   r   #   s   "   t   !   u   A   v       w   %   x      y      z      {   <   |      }   $   ~                                             &                                    ,                  =            0                        !                        
      (      *      5      D      2      	                  3            -            >            8            #      F                  6                  ?                              	      '                              4                  E      
                  9                              )                         C            /      B                              "                  :      7            +                              +            7      :                  "                              B      /            C                         )                              9                  
      E                  4                              '      	                              ?                  6                  F      #            8            >            -            3                  	      2      D      5      *      (      
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G                 F                    F                F                 F                 F                F                F                 rI                    lI                    pI 
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   H	˸   P		                                                                 		          	                	X	˸                                                        X		                                                  ^	                   ˸             	@^	                                             !   ˸          "          #          $          %          &                '          (          )   	       *             +                ,          -          .          /          0          1          2      G              4          5          6          7   h		             8          9          :          ;          <          =          >          ?          @          A          B          C          D          E          F          G          H          I          J          K          L          M          N          O   		    g             i                k          l                        o            e 	d^	          		    u              w      		       		    {                 }   	                3      		   \	      }    8	D^	            	   	˸                    		               	   ^	               		   ˸                	^	               	   ^	                	(	             I X         P                                                                                                                                                                            ' &     &         & &                                                                                                                             3I                 UI                I                     I                    G                +G                  G                   G                I X         P                                                                                                                                                                                                                                                                                                                                      ,I                 =I 
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                    G                F                    F                    F                F                F                   G                #G             X	"G                X	I                I                    a'                0  I X         P                                                                                                                                                                                                                                                                                                                                     I X         P                                                                                                                                                                                                                                                                                                                                     I                 I                    I                I                +?                ?                '                *?                &?                /?                %?                .?                D                  '                  D                  D                  D                 D                    D             D                 D                    D                    D 
                       D                D                    D                    D                    D                    D 
                       D                I                I                D                    I                D 
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        !                 "                 #                  $                                 %                 &                                                 '                                 (                           u                v                z    +                 ,                 -                 .                  /               "  0               $  1               &  2               (  3               *  4                               .  5               0  6               2  7               4  8               6  9               8  :               :  ;               <  <               >  =               @  >               B  ?               D  @               F  A               H  B               J  C               L  D               N  E                       Q  F       R  G       S  H       T  I       U  J       V  K       W  L       X  M       Y  N       Z  O       [  P       \  Q       ]  R       ^  S       _  T       `  U       a  V       b  W       c  X       d  Y       e  Z       f  [       g  \       h  ]       i  ^       j  _       k  `       l  a       m  b       n  c       o  d       p  e       q  f       r  g       s  h       t  i       u  j       v  k       w  l       x  m       y  n       z  o       {  p       |  q       }  r       ~  s         t         u         v         w         x         y         z         {         |         }         ~                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              w                                  x                                  y                                                 )         *       h          l         p              |          }          ~                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      E          \     x  p            Hn $  Q d L'     I          D592  y I   J                                            !/            k     7                                         Q               
      9   ]         t   t     &   >     yt                      t        !	          :3                                               <         
               H      Z        G= 
   Print(D592); sition(M592);                                    <                  '                      @                                          2             L=                                                                  (                                               }    h              $r @    @     '            ' 
                           %u                          (     (                         ' 
               ʸ' $      
                                                        %          J                 t           P      ˸<                                  <        ` T         G        P                 3    H    	'                                 <         H         l 4   `O	(     d   )	0    d      $    .	                  $                    6	                            $                            a                            '              ' 
      ,                  W       %   (  i       %   (  Z		ʸi'       r'                      L                         #'          (  &       '                      L                         '          (  '       &       }   (  &       ='                      L                X         1'          (  ]'       6'          (  L'       O'       '                      L               Ȟ X         '          (  '                      L               d          '       c   (  '       '       V       o   (  '                             b    %      (      %      (  A       t'              Z'       $       b'       '          (         ' 
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                     $   j    %      (  .'       !   (  V'               '       '       '                    %          ˸      '                   %                              '                            %   (  L       O               '          %   ' ,                                                                                                                            D d 0 О                     X                      L          h                l     ' 
                      $   '             x[		                                 '                           <                                 '                                 '           О                                                     '                                            4   8	    d   	`    d      $    8	D                  $                    6	                            $                                                                               u   \     \ r   r   @ l         U        '                                    '                         $     $                 ' .         $          (      o                  p        `a     m             q             r                        $     s        $  '                ' 
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      ,                         e       A'       2'                      L               d          K'          (  :'       D'                      L               ,                  v'          (  g'          (  d'               u'                      L               Н h         o'                      L               ؝          '                      L                         ['          (  '       G'                      L               l          n'       O   (  '       k'                      L                D         j'          (  P'       R'                      L                @         M'          (  S'       _'                      L               4 L         E'          (  '       B'                      L                p         X "         D 3                        $     c        Ԟ     d     0   ԟ     e                          #          (  $       #       #       $          (   $          (  
$               '       5   (         Y'                      L               Ĝ t         T'                      L               ؜ 0         F'          (  \'                      L                <         I'          (  ;'       ,'                      L               $          h'       g   (  7'       U'                      L                ܜ         '          (  8'       '                      L               8          H'          (  W'       <'                      L                 \         9'       9   (  Q'       &                      L                D         3'          (  '       ''                      L               ̜ \         &       A   (  ?'       '                      L                         ^'       	   (  N'       0'                      L               x 8         '       =   (  4'       &                      L               X М         ('          (  '       %'                      L                t         +'       !   (  *'       $'    %      (  !'       O   (  &'       )'                      L                         &          (   '       &                      L                          '          (  '       &                      L                         &       M   (  '       &                      L               `          &         (  &       '                      L               ț T         &       9   (  
'       &                      L               d (         &          (  &       &                      L                (         &          (  &       &                      L                         '          (  &       '                      L                         &       5   (  &       &          (  &       "'                      L                         '       @'                      L                         5'       '   (   '       /'                      L               Ԝ          >'          (  &       '                      L                         &          (  '       &                      L               ؛          '       A   (  '       -'                      L               L ,         '          (  '       &                      L                <         &       	   (  &       &                      L               ܚ $         &          (  &       &                      L                          &       =   (  &       &       '                      L               P H         '                      L                         &       g   (  	'       &                      L               ̛ $         '       ?   (  &       '                      L               l          &          (  &       u&                      L               8          y&       G   (  v&       P&                      L                ؙ         s&          (  [&       f&                      L               ̙ l         &          (  r&       L&                      L               | ș         h&          (  W&       g&                      L                \         %          (  %       %                      L                         %       '   (  %       %                      L               4 $         %       Y   (  %       %                      L               (          %          (  %       p%                      L                x         %         (  %       %                      L               L <         %          (  %       %       :&                      L                ܘ         9&       _&                      L               $          t&       	  (  Y&       X&                      L               Й d         G&       Q   (  N&       Q&                      L                8         R&       S   (  .&       c&                      L               H          4&          (  ?&       J&                      L               И          S&         (  &       b&       &                      L                X         &                      L                x         &       a   (  &       &                      L               4          &       #  (  &       &                      L                T         &          (  &       &                      L               @ Л         &          (  &       &                      L               ܛ ,         &       +   (  &       &                      L               L          &       /   (  &       &                      L               | L         &       3   (  &       &                      L               D 8         &       )   (  &       &                      L               H ؚ         E&          (  d&       a&                      L                         w&       U   (  >&       e&                      L               ܙ          H&       w   (  `&       i&                      L                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&       )&                      L                         &          (  &       &                      L               D p         %&          (  %       1&                      L                ܗ         (&       +   (  #&       &                      L                         &       -   (  &       ,&                      L               t 4         %       /   (   &       &                      L                          "&          (  %       &                      L                         %          (  &       %                      L                         &         (  &       %                      L               L          %       )   (  &       %                      L                T         &          (  %       	&                      L                          &       	   (  %       %                      L               d          &       E   (  %       %                      L               \          %       _   (  &       %                      L                         &          (  &       +&                      L                P         %       =   (  %       %                      L               X          
&       y   (  %       %                      L               ( t         %          (  &       %                      L               h 8         %       s   (  %       &                      L                          %       7   (  &       %                      L               З @         %          (  %       %                      L                l         %       {   (  %       %                      L                H         %          (  %       %                      L               D          %       #   (  %       %                      L               d          i%          (  '%       O%                      L                         Q%         (  V%       M%                      L               D X         H%          (  1%       Z%                      L                 Ĕ         A%          (  L%       %                      L                0         @%       G   (  7%       J%                      L                 ܔ         %       %  (  P%       $                      L               | @         C%          (  >%       0%                      L                         %       w   (   %       %%                      L               L          K%          (  ;%       G%                      L               ,          
%       Q   (  <%       B%                      L               (          %       U   (   %       +%                      L               <           .%       #   (  %       %                      L                `         3%       -   (  :%       4%                      L               ̔          %          (  (%       !%                      L                          %          (  %       =%                      L               t p         /%          (  &%       %                      L                         9%       /   (  %       %                      L                H         $          (  $%       #%                      L               ԓ          %       u   (  $       )%                      L               h          %          (  %       %                      L                8         ,%          (  5%       %                      L                Ԕ         %          (  %       $                      L               x l         %       S   (  %       "%                      L               P ,         %       _   (  %       $                      L                T         	%          (  $       $                      L               $          $         (  $       -%                      L               Г          $          (  $       %                      L               x          $       {   (  $       $                      L                         %       #   (  $       %                      L                P         $          (  %       $                      L               d d         %    J      (  $       $                      L               0          $          (  $       $                      L                         $       )   (  $       $                      L                         $          (  $       $                      L               ̒          $       ]   (  $       $                      L                x         $          (  $       $                      L                ē         $       $                      L               8 p         $          (  $       $                      L                 $         $       3   (  $       $                      L               ؒ          $          (  $       $                      L                           $          (  $       $                      L                         $       q   (  $       $                      L                         $          (  $       $                      L                t         $       C   (  $       $                      L                ܒ         $          (  $       $                      L                `         $          (  $       $                      L               D Ē         $       G   (  $       $                      L                         o$          (  $       $                      L                Ԓ         $       +   (  %                      L                         %       e   (  %                      L               H 8         |%          (  %       q%                      L                         %          (  %       %                      L               Ė 0         z%       M   (  %       %                      L                ,         %          (  s%       %                      L                ̕         }%          (  t%       N%                      L                Е         %       E   (  _%       %                      L                |         %       a   (  %       ~%                      L                          v%          (  h%       %                      L               ؕ          r%       +   (  f%       `%                      L               ȕ          X%       3   (  \%       {%                      L               ` p         ?%          (  ^%       b%                      L                x         %          (  [%       k%                      L               $ l         W%       7   (  y%       u%                      L               \          c%          (  ]%       j%                      L                t         R%    %      (  o%       e%                      L               H          a%       q   (  S%       l%                      L                L         Y%          (  %       g%                      L               d          T%       ?   (  8%       d%                      L               P          6%          (  n%       2%                      L               ؔ          E%       C   (  m%       I%                      L                         D%          (  F%       *%                      L                         O$          (  m$       V$                      L               <          D$       ;   (  \$       3$                      L                p         T$       m   (  /$       S$                      L               P          -$       s   (  R$       P$                      L                H         I$       W   (  N$       B$                      L               $ 8         *$       7   (  M$       $                      L                4         K$          (  ;$       9$                      L               ,          +$          (  C$       #                      L                         i$       [   (  ?$       6$                      L                         $       1   (  1$       $                      L               8 Đ         <$         (  Q$       5$                      L                D         $       ;   (  =$       F$                      L               0          >$         (  $$       A$                      L                         )$       I   (  &$       #                      L                         $          (  $       2$                      L               h l         $       1   (  ($       $                      L               4          %$       ;   (  0$       #$                      L                         #       I   (  .$       	$                      L                         '$          (  #       $                      L                p         $          (  $       $                      L               P d         #       '  (  4$       :$                      L                А         $           (  ,$       #                      L               H          #       $   (  #       #       %   (  #       $                      L                         #       &   (  #       #                      L                         #       (   (  #       #                      L               4          #       *   (  #               $          (  $                      L                D         !$                      L                (         #          (  $       #                      L                X         #          (  #       "$                      L                Џ         #       
   (  $       $                      L               ď @         #          (  #       $                      L                |         $          (  $       #                      L               `           $          (  #       #                      L               t T         #          (  $       #                      L                T         #          (  #       #                      L                ȏ         #       6   (  #       #                      L                ̎                 #                      L                         #                      L                X         J       #                      L                         #          (  $                      L                         #          (  #        $                      L                          #          (  #       #                      L               <          #           (  #       #                      L               \ `         #       "   (  #       #                      L               H          ]#       D   (  #       #                      L               t (         #       F   (  #       #                      L                0         `#       H   (  #       #                      L                t         #       J   (  #       #       L   (  #               x#       T   (  #       #                      L                $         #       V   (  #       z#       X   (  ,      #       8   (  #       #       :   (  #       #       #                      L               P          #       ,   (  #       #                      L                Ȏ         #       .   (  #       #                      L               l          #       0   (  #       #                      L                8         #       2   (  #       #                      L                         #       4   (  #       #                      L               d          2             m2 v:                O?                v  
                                   ʸn                                              o       #                      L                t         #                      L               0          #       <   (  #                      L               Ԏ          #       >   (  #       #                      L                         #       @   (  #       #                      L                Ď         #       B   (  #       #                      L                         o#                      L               u          k#       j   (  b#       p#                      L                         l#       l   (  r#                              L                ȍ         u#       n   (  \        c#                      L               ԍ p         2       o   (  #                              L               t          n#       p   (  }#       T#       r   (  +       w#       t   (  #                      L               \ 8         #                      L               x X         #       N   (  #       #                      L               (          #       P   (  #       |#                      L               P          #       R   (  v#       #                      L               l ؍         V#          (  S#       !#                      L               X L         U          (  X#       c                      L               Tu `         M          (  Q       N       #                      L               D  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          [$       [   (  _$       `$                      L               l |         Y$       G   (  $       U$                      L               d           l$       1   (  g$       h$                      L                         W$          (  w$       b$                      L               \ ܑ         8$       y   (  7$       f$                      L                ܐ         ' 8       ,    L          -            L .            h /    ` L       ܏ (            \ )             *    h         +     V       ̏ 4    Ğ         5    ԝ          6    Ȝ        x 7             0     4        1     6       ؏ 2    ě D        3     g           x        @ >     d        ?    p <       , @    t ?        8     	       $ 9    ( l       ԏ :    \ "       d <    P        ` E             F    l n       p G    `         H     &        A             B    | ,        C    $ \       L D    , ~        M    H         N    ̚ K       4 O    0 x        P             I    ȝ 
       Ў J    ȓ        ܎ K    ̗        ؎ L     (       , U    H R       H V    H         W             X             Q    x        h R     X       < S    ԛ 2        T             ]    p H        ^    \ S        _             `     f       T Y             Z            x [     U        \    T        p f    l :       Hu g            h h    h -       u i            ̍ b    | h        c             d             e     P       \ n    0 b       t o     s       Pu p      p        t q      X         j      @       u k      \         l       E        m              t v      Y       (t w    (        Xu x    ,        $X y    8        @u r     1       t s            t t     *       dt u    < v       $u ~      Ȑ !      lt               |t       X M       `]       \        pt z       9       tt {              t |       =       t }      ` '       s       W       t       d        (X               $t               t        a       s       4 +       `t               t         7       W        Q       t        #       @W       (        t               s              Pt       \        s       < %      t        w       W              W       Ę {       W               s       ؓ        tW       |        ]       @        X       Ȕ        0X       ԙ _       W                X       $        W       l        \W               W               W       X        W        5       W       h        W       H        W       ĕ        V        u       DW       В        XW       T q       V        C       W               W               W       ` i       V       T 3       E       Ԑ       V        G       <W       |        V       V       W        ]       V              V               PE       t [       hV              D              V       4        V               V        m       $E        W       tE                                    E        %     E      ;     E           4E                                              <                         X                                            `                 d                                   4                                             (                                                                  0              x     P     l        @     0                       h                         X     @              D          <              Ș               X          H     ؖ          ԗ     ȗ          ė     @ X 
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	    x  L     y                {  `            }               ~           Ğ       ԝ       Ȝ                              ě              x              p       t                (         \       P              l         `                     |         $       ,       H          ̚       0              ȝ               ̗              H       H                       x              ԛ              p       \                                             T       l              h                |                                0                  p                                                            (       ,       8                                  <                         X         \                                   `                 d                                J       4                                                  (                                                           Ę                         |                  Ȕ         ԙ                 $         l                           X                                  ĕ                          T                                    `         T                          |                                          t                                                                                                                                                                                                                                                                                                                                                                                                            0 u   v   w           z  @      |  X     H     x        ė     P        l        ԗ   X     @   Ș        0        D     ؖ          ȗ     <                   @     h                                              |     p                            ܖ     Ԗ          l        L          x          t   d           4                         ԕ                         $ p
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           O     @ `                         c     X |       Д              H      H                            4      0              p        x B                    r     ė              ܖ      P A             D        l       }       l F     D              ԗ      4                    X ^             ,                   @ /     Ș t                     0 >     (       @              ԕ      d         I     D j                                    ؖ              )            l             Ԗ              ȗ      T             <      $              
      T              |                     k              e      0                    	           T     L            (              @      X        h Z      p                                   @             t       8   	   .       ̓              L              ԑ      \              y                               X        ܓ        p        d                < o                    X       ̐     L       @              ,            ؐ       |                       "       #      $ $      p &       '      D ;        =      T a      @       pV       lE       @       E       tp       D                        !          "          #          $          %          &          '          (          )          *          +          ,          -          .          /          0          1          2          3          4          5          6          7          8          9          :          ;          <          =          >          ?          @          A          B          C          D          E          F          G          H          I          J          K          L          M          N          O          P          Q          R          S          T          U          V          W          X          Y          Z          [          \          ]          ^          _          `          a          b          c          d          e          f                      "          (  =       	                      L               t t                   (  A                             L               ht u         1          (                               L               t Dt         C          (         (                      L               u 4t                   (  3       '                      L               ,t t         -          (         I                      L               t s                   (                               L               xt Xt         >          (  $                             L               t t                   (          _          (         s#                      L                         f#                      L               P p                 e#                      L               ܍          o        v   (  i#       h#                      L                         [#       x   (  L       \#                      L               l 0u         D       z   (  Y#       R                      L               u d         d#       |   (  v        Z#                      L                         S       ~   (  y#       g                      L               Lu                    (                                L               tX  t                   (                               L               W t                   (  !       #                      L               s X                   (                   (  5   7   l                       L               4u Du         K          (                         L               ,u 8u         0           (          W#                      L               l          д           (  Z       ;                      L               @ hu         _#          (  9       T                      L               | t         !          (  @       +                      L               t  u         B          (  /       P                      L               u t         H          (  R#       4                      L                u H         5          (  &       7                      L               t t         O          (  J                             L               <u (u         ?          (  <       8                      L               t t         :          (  E       
                      L               t u         n           (         V                      L               4 \t         #   ˸	      k                         9   @      G   S   P         /   `      o   Y   p                                           O            ;                                         +  %         '                        a   0     C      @          P     c     `       [   p       =                    #           y          +                              E                                          }   0     {      @          P            `          p                                                                                                                    0         @          P          `     W   K   p                                                         U                                               /              0         @         P         `       	  p                                                                               (          .         $   &        <   >         4   6   0     L   N   @     D   F   P     \   ^   `     0O
	`V
	p        y          +                              E           }       ~                      }         {                         B   0      S
	`V
	           V m  4   `	(   x d   xh	0   p d      $    0	|E                  $                    6	                            $                                                                X                      L               s t         6                      L               |u  X                   (  ,                             L               t t                   (                               L               t s                   (  *       %                      L               Lt t                   (                               L               r W                   (                               L               s 8t                   (         )                      L               s 0t                   (  .       
                      L               t t                   (         	                      L               Tt  t                   (  0                             L               W t         `       &  (         M                      L               E F         _ .         $          (      o                  p        `a     m        ,     q             r                        $     s        $            
                             %      (  C                              L               E (E                               L               V E                                   $     $       |                                        L               t s                                      L               s <t                   (                               L               lW s                   (                               L               s W                   (                               L               X @t                   (         s                      L               Ht dW                   (  )                             L               W X                   (                               L               W V                   (                               L               W X                   (                               L               W 8X                   (                               L               X 4X                   (                               L               X s                   (                               L               W X                   (                               L               W W                   (                               L               W dX                   (                               L               W `W                   (                               L               TW W                   (                                L               W 0W                   (                               L               V W                   (                               L               W W                   (                               L               V V                   (                               L               hW $W                   (                               L               W ,W                   (                               L               LW V                   (                               L               |W PW                   (                               L               pW 8W                   (                               L               |V 4W                   (                               L               xW HW                   (                               L               V W                  (                               L               lV V                  (                               L               W W                  (                               L               XV V                  (                               L               V V                  (                               L                W V         e       
  (                               L               U V         n         (         g                      L               E V         S         (                               L               LE tV                  (  p                             L               V E         E         (                               L               E (W                  (  ^                             L               V xE                  (         I                      L               V V                  (                               L               `V V         H         (         T                      L                E \V                  (                               L                W V         c         (         1                      L               E V                   (  B       l                      L               dV E         K       "  (  a       k                      L               ,E E         w       $  (  :       m                      L               E D         _                      }  
                      4                      L               XE E         ' "      0                                   ,         U  g      F8      ww ww       5`5    [                      L               E E         ]                      L               F E         '                      L               8 0E         f                      L               \E <E                                      L               E xV         @$    ˸	      (   !                    <          ?   C   P   E       1   -   d   B       ,      x   F          D      H       J   K      L       7   M      N       t
	u
	   ˸        x                      
                     t
	}
	            k   ,         w   A   @  I       9      T  G          1   h  /          o   |                 _                    )  7     O               u             ]                         q     %         '                 0        a     D  C            X         Q   c   l  m         [           =                      #       g                +     3                             E                                   M   4              H              \               p                                        5                                i                   -                      $             8            L             `  e            t  W                   S                                              U                                                  (            <            P             d            x  	      
                                     
                                              (   *             "     &       :   <   ,  0       4   6   @  J       N   @   T  D       X   Z   h  ^       R   T   |  h       l   n     b       f       z       ~   p     t                                                                                        0               D               X               l                                                                       
                   t  $                  3                   (                                 $          `E          (                                       @        )                                   
                             _     P |a `         '      	      k   !      s   w   A   )   I      9        G   S      1      /         o   Y                 _          -        )  7      O           ;   u            ]                      q   +  %        '                      a     Q  C                   Q   c     m        [          =                    #     g      y         +     3                          E              ?       	         M        }        {                                                              5                              i                 -                                                      e             W   K              S                                          U                                           /                                           	     
                                 
                                              (   *   ,     .     "   $   &   8   :   <   >   0   2   4   6   H   J   L   N   @   B   D   F   X   Z   \   ^   P   R   T   V   h   j   l   n   `   b   d   f     x   z   |   ~   p   r   t   v                                                                                                                                                                                                        
                                 (  *  ,  .                              1                `    *          < v           ԙ                     X M       Ğ     \        ԝ      9       Ȝ      $   <˸     =                    <           P       ě     d               x                                  a                 4        t                                          Q     \      #   ,             ( @           T             l h       |                                            |               $   Ę                        H     ؓ                  | 0      0     D             X  Ȕ        l          _                               $                         H                                   X                      x     4             H  H        \             p        u                 В       \       q                                                              `            $  3          T 8         L          G   `       |    t                      ]           |                               t [                         0                  (  4         <             P           m   d           x                                                                     ,     ;                      ,            @              T          h      < |                                X                                                         0  `         D      X      d l                                                                   "   <˸              p             @          P      `           p                                                                                                         0     x @         P         `     @ p                                                                  X      @                    D        0         @         P     Ș `         p         X                               ԗ                   ė      @            x  L                0          @         P     `        p                                              Ğ                      Ȝ                         0         @     P       ě `         p            x                      p                                               \           0     @        P         `     p         `                                              $                       H             0       0                                              <         u                                           <        v                k                                               (        k                               7                     /J                              X  
            
			                                                       (                                          dq                                                           2         (?                                 <         ~         )                                         <        q Z         J                                 <        l\ $B         r)                                 (        x_ p         |                                 (        |          z                                         \          K                                  ,         Μ                                          <        P          b                                 (        e                                                   p          "           {            +                                             H X                                           0 	     3                                         P h         T     p        rK    0
  < ؛ p                                                  <         1                                                   <         $0         >                                  <        /          M     0 0     r                                  (        41          r                                 01     T	ʸ0         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	                             <               (             
	               P                            	x                  h
	                 
	
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	 
	@   ˸            T             @ h         p)     |  
	    6	              $   G       
	8
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	             8
	    (
	
	          0
 $   H       P
	
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	    `	˸  H     
	e	  l     
	
	              P
	    7	               P
	   	    8
	
	  
	             $     ,          
	     ˸   4         $    H          
	6	\             p  
	       
	  (	    
	
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	    `	
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	  47	             \
        F   $  
	    ,7	   8          l) $ L  E       
	
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	t  
	                                                  0
	7	              
	    ,
	            $               
	0
	            H
 (             
	<  A	           P          A   d  
	    e	˸x                 
	    o	ʸ       0
		                           
	  
	                          0
	    6	                 0
	,  7	          @      
	7	T            h  
	          |         $              
		            X              
	  7	                     >     
	    P7	              $   !       
	
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	           l  
	    	,
	                                            
	  7	                       B       c     ˸                 -              ( x         F (         `8          8    p      R    P      \ P   @      G <         `X (         X P         \    0      ] *       	˸      
	˸      0
	 
	                         0           @             P     H
	
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	 
	                 $         
	 
	      8      (A	                  
	x
	                 (
	x
	                  $    0     0
	
	@            P     $    `     0
	
	p      (      	˸                      @      X \)      
	8
	                 $         
	P
	       \       7	            ( 0           @     P
	0
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	ʸp     	
	                 HW	 ˸              >            <A	                 6            
		      
	h
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	p
	0            @     $    P     h
	8
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	
	                                                     
	8
	        |1      7          h
	H
	      8
	h
	                 h
	
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	p
	`             p     T7	                         @             
	(
	                 $         
	p
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                 J                               	             C#                                 <        (
 7         \                 3                               [                  kJ                           
      w                 `                    -              '          1                     h?                p  X         P       d         d D d d                 h5                             p     e     lC                            x* 0     +   	 \3 8         h         7 , ~ h ` V d   4     Hb         ll     u         h h       9                 d             0  4 X         P                d D d d                 h5                             p     e     lC                            x* 0     +   	 \3 8         h         7 , ~ h ` V d   4     Hb         ll     u         h h       9                 d             0 	
Z0                                     `l                                                   ׌                  u              '  T	           (    p 	T)                                                                          }                 x 
                          S3                2             >                              '  h' -     "J T                      t            |5 $ P      ~ ( C     X u                   $                           v3             '        $ <  8                                                        E                 uJ                @                                                                                                       J                  P      5  t        K                   PM                                                             
         95          
      h             
  M                                                   S                 f                 o                                 Q5                                                      ,?                !                         C     C       -          !                 S                 J                D                  
             "   !    . (        $                             `  X         P                                                                                                                                                                                                                                                                                                                                       \                                  .                  1]                 3                     a              4                
   y                                            Y3                 F                0                 0                 >                S                 ܌                                        uV                 x                  E|                    Ц                     #             o?                                                                     N)                                                    *3                '             >                +                                      b0                                      J             
   9                3                gJ                    /                J                                  ӝ                  G                 0                                    o                 =                 0                    |J                                  )                                   <J                                 @                K                +                 $                @                	2                    ,3                2                            J                                        2                             |                     :              0                 g                 '              C                ˸5                                 	J                k                                  S                               9             !             J                
                Y                 O                                  G          
      x           
   b?                    Ȃ                 
                             ?             *                                    @                0             ٦                 v                     f?                    u                 ;                l
                &                r3             ly           
                                     R3                U=                5                                              4                Q                    0                 8                R=                                 <         )                         !             9                                 <                  a                                 <        4 )         rJ       5          
                    Z5                &                                  g                 }S                 {[                                                  O 
                                                                                      g          
      '                    o                  A                    2                                  
                	                                                    
                                                          u                 D                               |                                                8                            
         "           
         u           
                    j                l                                                                                               <                     }                  I                 n:             }                    }              }                 k                                                                        5               
                                                   $ H		J                    4                 r                                    :                                      ă                  Ǟ                                  4                vl                                      =                                    ^                  0 
                                      C                 -                 Y                                      l                  Ӄ                     }                                  }                                       }                 l                                  1                                                         F                 V                 hl                                                    )                  H                  M                  `                 A                Ț                                                   G                  V                                  K                                                                              E                 2                             X                                                                     4                                                      H                                    d                                   >r                 S                 2             B                  }                                      ?                 }                  ;                                      U                     H                 T                  E                     P                     H                     8                 L                 ,                     }                  d                 )                 k                  X                                   =                     ,                 C                                   I                  &                 D                                          9                 h              %                                  Q                 :                 6                 9                 7                 -u                                      g                 G                 b                     R                 i                    X                                    j3                                   T                                       J                                  T                 6                    Q                 P                 P                  Qs                                                    7                 i                     K                  X                     W                     Y                                      e                 G                  =                 M                 O                 :                 V1                                  ޳                 &                  H_                 B                 N                  C                  ;                 L                     2                ?                 2                 =                 ݳ                 I                 H                     ?                 2                 ;                 q:             [                `                     [                    J                  Z                                   @                                       *              ?                 `:                +                              G                                    [r                                                         .                                                     J                  P      5  t        K            L          I            "                                     Z                o                     s                                   *                  (                   M                 ʸ                    
                 t:                    43                                                     P                  B9                   2                                  ֝                         e                 #                                   e2             `b	D3                b	                                B~                 I                 c	                    9                                      \=                	C3                p N9                    J                2                                o              Nn                                                     n                                                           t                 $	TJ                 ȁ                     g                     x                 0                    s5              b                 !                r              /       t                  $ P   F   t           u                   $                        F                     Q                    h                                    3 T                               	   
                                                                      !   "   #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   4   5   6   7   8   9   :   ;   <   =   >   ?   @   A   B   C   D   E      u3                 9                /                     @1                4	                   v                    T                                      F?                   v                 0                                    ;             3                                   v                |+	             8                                     ?                                    E=                $                  :                                     9                 -                                                  X [3                                     f                                                         ?                 /                0                Y2             	O#                                               -                                                  5                 ~5                x 
                   ;o      
               l }                                7= X         P                                                                                                                                                                                                                                                                                                                                        >    0o \    F   P   $ t      rG       v              $ ' =    P                             w               E                   
                           0                 m                                  7                                 o           P   7     8  < - t_     a z                  t s  ) 8 v  a   )   TC  <E           |          * d(     T 0    -  `u ( 0    T ,          L @ H   (            ,d          7    P    T     , T                  P     HM X      h   8 4  X( Lt  < @ 8 + t L  4I  Ȥ ` h |) T* 4 $d  /  8  $  \      p* Df      H0   g  s  (  Q                          p     {                                 J                 g                (             q                 Z?                   d0                <?              {0                                      2 
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                           s        t                  $ P        7         u                   $                                                             (         $g                `?                                         P0                                 0                K                K                K                                    K                K                    e)                K                K                 >0                K                    K                                       K                                     K                    R     N              xK                 G1               /                    	        Ž              I        T                oK                 f                      Z   ?   fK                                    =                s                 
                              ' $         ${         v >       }                                                  (        dl                                   ,             VK                 >K                50                PK                    MK                 JK             f                 :0             IK                                 EK                                  t                                 @K                                    c                 W0                                     DK                                                   <0                                  GK                    BK                AK                '                7K                ٜ                 G                 d                K0                   2      C 8  p $                                                  D                    9K                    d                  8K                 h                 D                                 DI                8a                 s                V                    u                                   l                '                                 ƶ                 2K                    p                c                  E                    -K                    :                                                     R                (K                3K                +K                &K                O                e                }2                     }                 U                 )K                                    v                6                           0 \     F                    *e                 g                   l                          !K                                H       |                   C                 B                     "K                ݶ                 '                 K                s                                             ;                    d            s                v                         n       ~                    J                W                    K                                                                   T1                              9 K                    2                        +     v              2                                  <        u $                U"             </    P h       Y              :                / 
                             >                         q                 t                               +1    0         K                                                  Ň                 J                    o                I"                ĉ                                                        /                 K                                                     2                 t              K                              (a                 G"                K                   K                T                          1        K                    J                    K                                    K                 J                 J                                                     J                    !                J                ZF             W                 {                J                9                  x                                 J                 j                  J             J                            O        J                J             J                                                  ږ                                     u                     q                  l             0                                    J                )                ,                J                )                 J                9                P                 m:                                 <                                             )                                v)             x)                ~)                
                    J                J                {)                                                   w)                
                                                            4                 <      8e          J                                                  ( P   P    u                  	y)                   B    G        J                 )                 -                 N
                 8        D/ $        =                                 #                                  (         2                                  0                                              )                                 2                                                                 J                 -              ќ                    d        r                                                                                  :                                 /                U                        ,k     l                        e                J                 =                                 )                                                                      r              /                 U                J                    J                    h                                                   <                                                   <        \ |                                 <    ;                                     æ                                                       ? 
                    55                T                      N      2                w            8
            _:                2                                                 <        1 L         J                                 (        4 <         D        V                 G                                q                    /                                     p                    $                                 ss                 Zy                               y                                                   3                                 d=                 K                8                             t     -5                i                 r                xJ                                  !                Lu                 s@                 !                                                 N              C                 H         $ wJ                           :                v                   "C                 
                                          ,X        4 $                                         ܢ                 z                                                                    ;                 1                     5             5                                  U1                                  W                 5                 f                       
                                                                                        dK          
                         .                 M                 <                               P                                   a                 *                   
                c     j}                                                  f                 J                 9                                     2                                      ~                                                           %                  x                 *                 P                                   l                 
                 u                                      }                  D~                    m                                                  Y                                                        ~                 |                 |                  !                  ^s                     N3                 9                                                                      b                 u                     e                 {                                Io                                  y3             ]              4	                 !                 Ns                                                        f                                      4          
   	   ;u           
      >       %    ٬                 e 
               X     3                 2                           $                                     p                  g                                      0        t           PF X $ P      p 8      u u                   $                                   .                     S`                    F                G                                     ^                                   t                  h                                   )                                  T                 s                 I                                                                    -                 rs                     u                                   b                                                   [s                                                                       *                  l                 -                  }                                                 ~                 ]}                                     u                     l                    ~                 l                  >u                  9                  q                 Bs                                      e              5                     K}                     U}                     5s                    }                                                    U                                                        E}                  m                 m                                                                                           q                                            1 $        l                                                       }                 Ճ              _                                   ;}                                      }                  .                 u                  dl                               v                     ֈ              }                     }                  f              l                 f                                  }                                                   2                                                          }:                         * $ 2       f}                  6       P      	o D                                         X     t                                     
                                          T)     W                                     l         t                                      <)                                     T5                                                                                    @     \<                                          l                                     |l     42                                     pL     D                                     x         $                                 l1     h                                                  X                             5                     (                     )                                          dm                                          0     C                                     n             l                                  l                                     n         L                                 Lm     |                                     ,     8L                                     ,m                     m                          5                                     `m             `                                  [                                     Pi     P*                                          ز                                     L     Dn                                     X             6                             02     hL                                     `                                          tO     n                                     t)                     m                     )                                          m             l                             Lm     (*                                                                                            HL                                                              5              &                                     n      L                                     `m     L                                     <             ,)                             l     f                                                          )                     L                                          6                                          )     @%                                                                                                                         l                                                                                    &                     H+                     p                                                                                    8                                          е                                                       <                                                                                                                      D                                                  0                             /     P                                                                                     |                                     	                                            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d    ,     k G *     [                 
                     2                 p              V                 J                    L                 8C                    N#                    Zn                                                                    2)                0                 z                0                                                      *#                I                kK                                                                l0                                                      H                 0                x                 B                                 G             '                    I                                                                            P   $ 8 x     e              2                                                       ?V                                5                                                5                                         מ                 L              v                 )                                    2                        x  
                    $	]                                  On                           J                  P      5  t        K                                Q                                                      ^3                ]                 =                 ʸ4             ?                                                     r2                   C                    zJ          
      0                    T                           $                                  <        l @b                                   L                                              (     (        Ь          
   4               q'                                  P   P   x- L         K     ʸ      
                          J                                          (     (       l(          m          
      !                                                 (?       j <                     8) (R @    8 H   P5                   m        l $ B                                 <         4         /                 )G                    *                                  @       d p                                           <        (               b       [                        H                    ;                                  @       6 x         K                                  @                 _            $                                      0G                    T                Ha  
                        /G                I                      <      ^                  -C                8G                 L        $G                2@                9@                         J                                                                        g                     L                  4G                    e                     
                           9G                H                                1                                  (         <                                               >                W                                  <                        \                |        2G                H                @                 /                  ?                                ("                 @                            @                                                   (         |                                     Hu         H                                  @                 P                     :                 H 
                       pD                N 
                    l!	`1                                                                                      H 
                   D	     ,G                                     l                 Z
                                     v?                    FG                 X                  G                  
                           X                                                   <         <         ?     j                       )                                                                 \                                  <        ̸ @         $     p p `  O        g              H                  
                     H                H                                 b                                 G                                  <        | ظ                                           <        h l              f       |        F                                                                                           H                                         \                  
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                 M 2         *   	                         T6 P6                                                     L6                           @6 86 46 $6                                  i                                                       @       |                                        #              ,                         Ը                                                                                           !r                    
                    h1                H                    5G                w                     H 
                        H                   6G                             H                   [G                     
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                                      X                                    k     N     l                 [                Q                jD                         a                 O                                     ?                ? 
                          -@                         @                   F                 *        y                @                   @                 ?                    |  
                    ڈ                  q                                         
                      G}                 ? 2         *                                                                                                                                                                                 gK                    ?                ?                   ?             @  ? 
               p!	W	  ߶                     ?                 ? 
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                       2                J                X@                   \@                d@ 
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                         2                 S@                5@                 #@                 K 
                        2         *           # # 4#  X#       h      6   	 # l# D l     #          X b () T  t  `	  p	             T                                          <         (         p                                  (        п P                                         d                                                     Lb                 yM                 -  
                       Ia                                                   @       t Ķ                                           <        `                                   ܹ                                                                   <        \ d                 ~                         P                               5                                  (        D L                                           @        H         T                +                g                Q                                  (                  B     ȶ      &        r              q                                                    <        0 ж                                           <                  b             T      f                             L  
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               |                                       BJ                 i                                  <        @          y     ^                       [@                Z@ 
                    C@             P@                O@                    E             ]@                    c@ 
                        Y@                 3                `@ 
                    B  2         *          D  <   $  $# D     (       X  #    	              #    H$   <    T   X <	 	           $       @                   |)                                                                            ^=                                                      <         t                 v                                  (        ) X                 }     \               <@                    @@             n                   H@                                      {@ 
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@ 
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                       S                                2                                  q                         D@                    O                                  @       ̵ h)         k                                  <         $               |   i              h         _=                    |                                  <                                                            (                  u                         ص     *K                    (@ 
                ~                     {     F   ʸ@ 
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                    h@ 2         *           4  ̥                  T< | ܇ L     l         H p  d p  l h p + ` 8       ,     P (      ?                    nI                    ?                ?                ?                ?                   ? 
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               Pi		ʸnG                    8I                 ?                    2I                (C 
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               x f	]G                hG                    eG                    DG                    G                    M                @  \      >   @  (                 M                         ?                 ? 2         *                                                                    -      -                                                               *C                bG                 aG                    VG                    RG 2         *                      L h                                                             x $     ' p                                 <                      d?                    n?                    ;?                    (                    > 
               (o		ʸdG 2         *                        T                                                               X       .  `                         ğ X                     QG                   M 
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                   X     '                 C                    K                 kG 2         *   x             <      $                                                                    x  `                          lT .     t          ?                    ' 
                   \     I                 \G                    OG                 ? 2         *                        |  -                         .                              ' p      .  $ t                          P               D                 WG                8     >   @  CG                 M                    G                 m        '                 M 2         *                        $ b                                                                                                                     ,                      !M 2         *                                                                       С                                                                                                         M                (                M                 M 
                   06     M                    gG 2         *                   |                                                                     h     x ` . |                                            M                     @   ~ M                    M                   M                 M                            NG 2         *                   -     0                                                                  |      l 4                                  x6                     l( 2         *                   8-     - 8                                                                             l '                                 P @                     vM                ;(                     |  <l	M                    M                ~M                Z        M 2         *                       D                                                                                                         t6 d6                                         M                    M 2         *                       \                                                                                                                                                         W(                    XM 
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               `'         &M                    )M                 fM                 )                 o(                S?                    q0                    D 
                        yM 2         *                                                   5                                                     5                                                                  bM                             	Q(                `M                ^M                ]M                    dM 2         *   z	                                                Ԡ                                                                                                                                 cM                hM 2         *                                                       5                 5 5                                                                                                 lM                    nM 2         *                                                                   5                                                                                                             Z( 2         *                                                                           l5                                                                                                     U0                    x(                    OM 2         *   `'                                                                         5                                                                                                 VM 2         *                                                                                   `5                                                                                               
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? 2         *                                                                                                                                                                                0 2         *                                                                                                                                                               ԣ                 [? 2         *                                                                                                                                                                               ( 2         *                                                                                                                                                                                A? 2         *                                                                                                                                                                                ! l      
   
   X      x 4  H{      } \u )  (  ؛ \  | 4z  x  7 ) s ,R ( W     l L $  7  
     	   $v dt    x&     d8           ;          E Ф  p.      8      z . Ts Dk                 4  h x 8  0     8 u c E LC X                            4)                2                3                                    $ 
       d                                                       x              $ 
   d                                                     <        P                                            (                                                                                                       <        P                                           <        T L                                           (                                                          	 T         G/                        ȥ                                            e     )    k         f                                        |~ $\         c                             @?     4       P   $       D                 v              _J                                               4                K                                              J                    2                   4                G                                              G                 cJ                              !                                                                                                   7                                                          8 X         P       s  R g   h      j h)                    f V \  Ln LV ̦   7 0)          , s s  c * \ t8 c b c U         (   pf  <  X h   . U $R  d     i HV  c <i 8k 8F j  d    ,     k G *     R                                     :                                   ju                 J                                                              >                q  X         P                                                                                                                                                                                                                                                                                                                                   ˸%G                   J                  P      5  t        K                             8                Y                  b                                   2J                               	Ң                 R             '  9 l d                                   l                                      -3                4 "                  J                  P      5  t        K            L     b     I            hQ    r                  !                 1                                  z  
                   <* ʸ             XX                  id                    _K                #              8                ͞                     4                   U                                      'K                 "                t5                              (                     $/                2                                 O                    #0                    T                                  h5                4?                N=                    ˀ                  V3                 3                 h 5                                    $                                                               c5                   0 
                                 ڪ              	   k                                  +V                               	   i                                                	   5                    @                 q              	   s                 a                               	   a                 >                 Z                 N                 ,I                 y                 {V                 \                 f
                                  l a3                                                     G                Y1                             0                #                    *             '              9                                                                    n
          
         C                 g                3                $           P             h( O  z   ܆ t ܣ lG Tt                 )   2 ((   z   0 d x l   p3 X \     P h \  p 4V      l{ t+ ) d hV   pr X ( x p 8 P2 /  / 3     t q q l D L d~ k          `X D       h ( d   < T/   u                   l     p 	 $ 4 L s `  , 0  ~ T    +  $ X l X  HX l h  $2    < / G H{ 0 Ԛ /  [   d     Q  Ć   X   h                          P     { T           G                                L                    8                 ?          
      H                                2                 ς                    gv                 lv                 sv                                                        t                 dx                 x                  &J                "                     1                     5                                        g0                {                     N1                h           
              
      sK          
                    h H- ?                M                 2                 &V                                 3                3                (                    J                  P      5  t        K                   H)          
                
      c                                   )          
      X          
      Jv                                      J                  P      5  t        K            L          I            .                       t           hn       0 8f         {                    #5                 2             (                ?                [5             ^                     b1                 {                                                   2                    3                 E                     J                  P      5  t        K            L     L     I                  *  U z *                  
               2                        
               K                 L3                   a                K                Y                                   K                 2                m         m    !                *)                i0             0                      
                                                                              A                 As                                  /                                  J          
      D                J                 4                x                                    4             C                 9                 ſ                    ]J                >                ]                  B                                                                 h                 C                2                z                j                2?                5                                    =   5                              D                                                           <                 _                 (|                                                       z                 D5                5                >                                 0?                 0                )                 E                 /y              3                   m3                     5                              0                4                5                5                 (k                 ۆ                 !                                        
5                                 O5                   o                  4 X         P                                                                                                                                                                                                                                                                                                                                   ˸x                 IT              0                                                                     o2                8                 B                O                                              !          
                 
                      *                                           o                                                                      C             -                                2                                    1                HX                                     Y0                e"                                  ev  l      
   
           0     < 9     Y  Lp @    @ 8i $( ] h |I l      8  + c [   (  4v u t  X8       Ԉ    <     \  p \ P      L x     h pt  l[ < r `;    X+ U  l    g  X + @   @~ )  c                      @  P    Qu  l      
   
                                                                                                                                                                                                                                                                                                                                                                                         (	                 |'                )?                '? 
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                   f P   V=                    ns                 '                                  ,                                                        l      
   
          t) P h l 8 V L F  / @  Pr < 4( ( ) 8 ) @  j 5 ܛ  p 0t  8   D 9  @ 5  3  D   ܢ l* @7 d   (k   T  7      f   8     (  T ` / |- L(  <     HC   P]   l   8 x xh t 1 T   ,b          p ; j        8 i      ?                   X                                 4                                    
                                   
k                                                                    ?                                 25                4                                       1                i                 x                  0             ؼ                 i                                                                     $                 Ay                               8          
                           <                                  3             
   1                G             2                e                                                       J          
       )                               ?    ?                 0                      J        D                 ??                ?                >             PJ                 P     f         B?                 >                  )                 4#                     1       
        c0                 >                 q?                \0                9)                    v0                 ?                 ;)                #?                 N                      v D                  4     4
    ?                    ."                 
               h                                  <        h 8         J             e                 ]         ]     4                                 <        @X                                   0 
                      
               `Qʸ        G?                 M?                                     c                     C      @0    
1       r              /0                K                I)             K                K                   K                    K             K                    K                    0                    K                K                l    	 $
 ?   K                                 zK                    r        &1                        pK                0                            cs                                  <         xk                                           <        (l xr         
                        `l              .                                 (        Dg @                                       dr     x                                                < 4         $       7                       p                   ,                                 <        u                                           <        Dl          F       !     
   ˸                                         (        l `         %/                3                  f                                 .                =?                !                b                 f              
                                 <        d                                            <                                                           (        x L         s                                                                                       Tk               k                        s        r                                            <         k                                          <                  <       
      ˸B       r                                  (        P+                                   pl     z                                                          k                                         j                    7s                                  <        hl q         Lr                                  <        h Xk                      0  ˸        r                                  (        k xl                                  k          k                                                   k k              hk                        r                  t                                  <        ll 4         r                                  <        u \k                       u ˸        sr                                  (        Pk <v                                                  |u <         Z                                         |r u                 S               o                            r                                  <        Dv          r                                  <        dk Hk                 r     8 x ˸r                                          (        \ (                                  Du          X )       _      N                                 <        + 8s         z)                                 <        = Ĩ         Y                                 (        H          1                                          hf         1/                                 <         R               ļ ˸                         L     /    T         ;9                                 <        D <	                                           (        (                                                    H         j                                 <                  Hb       ˸~                             wr     	                                           <         (0                                           (                                                            <1          u                                 <        
          }/                                       	     O              1                                  <        d l                                      #1    \d         r                                          ,1         C1                                 <         $                 >3                                 <        \          2                                 <                  7     @  ʸ!                z2                        f                  q                        0                                                    <        D |         e                                  <        @1          q                                         <                  w                                 <        H1                                            (         
                                  `                   [                                 <                                 a       !                                0           8                        X         P                                                                                                                                                                                                                                                                                                                                      ʸ                .                                    `
                                                      I
                 >                                                 ,                                                                             V
                                                      i
                    T
                    P
                           P      d                                                                                                 P                                                      (                                                                                                       h <            |     d                                                                                             q                                   +             |W          h +                             7                                             ̆   7             |     x ` 7         d                                                                                                                                                  d +     4,                     q h      (P +     X                             X, H, 2 8,                             t+     + ' h[             d                                                                                                 ,                                                     7                     )                                                     + P p                                                                             d                                                                                                                         @v                  +                         D\ H -  k     P ,     Q                     Xa  ,         a u                             +     \ , Q                     d                                                                                                                                     , a P\                                             |^   \                                         $)                             %     7 ] p                         d                                                                                                             0 |                 u t                                         V p, u     ,                                      - a                             ,     Ha q $-                             d                                                         p.         .                             $                                                                       0.         @                                             6                        @. . .                                 d                                                                 ,                 ds X- f                          .                  a , X.  <. .     - 4     u                                   . D. X
 l. - .             ,      -                                      d     $                         p                                                              l                 P ,                     D p Q  +      p     |                          D      dq                             u      h                                          d                                                 + < P9                                                         + D,                                             <,         x Q                                                               -     p  <e                                                 d                                             ] إ                                     +                 $                      s \ C , u     0            o                 d         `+ x, \ ܥ                          hB (q                                                      d                                          x.                                  P.                 Hd o                         - 8 d d     ,. |8     -     T . 6 hC 8 X)         x xf - 7                     .     4 . P                                                         d                                                                                                                                  @) 4-                                          | o DF                                                                                                                                             d                     u                               .     ,                             ,             l @- ,         u                                     Q     P) , \ - )                                                                                                                  d                  H                     O ~                 + +     + -                                          8 \a [                                           - d  +             (-       R ,                                                                                     d             Ds                                                         p\ <                                             \ q d+ @                                         T z @ Td                      |b                                                                                                           d +                             l                 Z A                          p p e     H\ Կ                        W p         X+ , Te                         4+     ) 8+ u                                              k lk         Bt        }                                  <        Hu          U                                  <        k l                                  Tu u     s                                          (        Lk \                                                  k                                  4     k                        Hl                                      u                                  <        L u         Ԇ                                  <        k (:                      P u ,˸        Q                                  (        ԧ          ~3       5               Q3       P                          @                                             P                ~                                  <        \ k                                           <        v                       l u ,˸                                          (        pX H         ^5       =5               0       P           /L                                                   2                            53         #        Y                                 <        l           
                                 <        @ 
              ( d                                              (                   ]5       M5               3       P           1                        p                                               x         *             H5       0                                 <        T0 d                                           <                  .5    < 8     _5       2                                 (         |         5       65               /      P                                         E5                                        Db t             u         5       >                                 <        d           K                                 <        D                     </ 4 ,˸a                                          (        82          2       5               .       P                                         63                                         `         Ǿ     P                /                                 <                                                    <                   o3             D ,˸	5       d3                                 (         $         0       V                X3      P           s                         D     3                                                  &G    u         2                                         <        4 (         2                                 <                   9       4    D , ,˸        })                                 (         X                4       /            L  ʸa                              W5                                                  n5    u         t3       ]2                                 <                  4                                 <         L         3             t ,˸F/                                         (                  G5                        5     0           ʸ                              |                                                  4    k                0                                  <                  0                                 <        0          ?            < H ,˸N/       4                                 (        @\ 8         @5                              P           (3                                        P          3             *               0       ./        4                                 <        X l         2                                 <        ` @         0       .1    T l ,˸=        |                                  (         H         0                        `     3                               + 
                                                                  ,                                           <         G              7   o      f      7      0            i5                        t     S                                  <         p         2       p                                 (        02          u5       /               *      P           j                             P3                                                       1         ĥ        2                                 <                  81                                 <                  2             d ,˸/       2                                 (        D t         J                             P           W3                             2                                                  s    \                6                                 <                                                    <         |         4              ,˸{5       :                                 (        xv          0                       \5      P           k5                                                                       *         h3             0       x3                                 <         <z                                           <         D2                5       ,˸*       2                                 (        \          <5       5               4      P           5                        \     *G                                        @/ |         K    L                q)                                 <        |                                            <                  c2       83     ĥ (˸3                                         (         `         /       4               $5      P                                        0                                                  0    2                                                   <        < ;         2                                 <        X H         5       z3    d , (˸4       ?                                  (         H         Y
       i                       P            2                        t                                             # @         H                    :/                                 <        4          V                                  <        p H                 v    X  (˸4       5                                 (        1          t       2               2      P                                    p     +5                                        t d)         ]3    $         w5                                        <         ,
         8                                 <        t 1         u       I      (˸4       5                                 (        '          e3       }3               2       P           #/                        8                                              t 	                      )5       2                                 <        ,          (G                                 <                  A5       5      (˸5                                        (         0         2       0               x5    "  P                                    \     0/                                        X          2             >5       3                                 <                  b3                                 <        t           H3       0      (˸        2                                 (                         4               3    $  P                                         3                                         |         ,5    4         j5                                         <        $                                           <        @ @*         J            6 v (˸0                                         (                  0       0               @    &  P                                    ܌                                               2         75             2       	                                  <                  5                                 <         4         5       J3     $$ (˸4                                         (        (                  2               F3    (  P           0                             J                                        x          2                    0                                 <        D          4                                 <                  G9       85    D  $˸/       7#                                 (         x         v                              %   P           0                        R     3                                         X                       :5       SJ                                 <                  M3                                 <        t D         *       k2    4 L) $˸0       5                                 (         ,         *                      ,     	   %   P           *                             J5                                        h 4         5    Ȫ         0       U9                                 <                  B5                                 <                  :       *     T $˸3                                         (        t D                2           c     %   P                                    ]     4                                        d @         /             L       X                                  <         p         2                                 <         t                      , b $˸J                                         (        ^ *                             x2    %   P                                   <                                              P C         5    lb         4C                                         <         p0         15                                 <        [          a        y:     [ $˸2       l                                 (                         2              Q        <3       2                              i3                                         0         "             1C       2                                 <                  u:                                 <        H b         X        ^:       ˸L5       5                                 (        x 0         i                
               	ʸ                              c                                         T          U3             r5       5                                 <                  5                                 <                  4       Q     8   ˸O                                          (        TF ?         t                 [                                                '        / 
               j  4                                 <                                                    <                  %3       3       ˸W:       C                                 (          \         z T     0  0  < 8  Q `d  H l    g |   0 p  8 0  <0 /      0  $k ( k l k @ <k Tl `    k ̧ h l t 0 /    \  p  @    4 2    (  * < (  x   \  7	?y                 x                    }f  
                       *1                                 <        x          2         g2       X                                  (                    
   F                "                   G#                           g?                                                      (5                z5                n                     Ҟ                                  v                 Ym  
                  	p	[                                   ˔  
                       3                    2                                 4                    o                 4                 rD 2         *   H                              8                                                                                                                                         kD                !Y                      2         *                                                                                Lc                                                                                             ?                ZD                    b                 / 
                           ? 2         *                   4     02                                                               `       D 7                             \                      V 2         *           ,                         D \                                     1                                                                                             :G 2         *   P      \                          &      `c h      3 |   `                                     	  \   P]         L     d     i                ( 
                3     a                                                    JG 
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L                    p                                 J                                  !                 b5                                 F"                 t        t           S % $ P      t        u                   $                                                    hs                                   u0             2                ,                 {                 x              
                 	      %J                              
                       u                                                c                 k              v[                                                O                 y5                u                 E             G              	   1             t              !                Y                                  j                 s              	                     w                  yK                C 
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 (     
   P   d                                                                         t                         d +             \                               `                                       0         X                  W p F             Te                h      D} 8     d                             u s 0 H{ d                 F g  X{     {         T      Q     `l )         (v + h <                     h 8     /   }      g        a  . 6 } j 0          ( t                                                  d                         d ,  \{                  8n   9 X     `p U  d 
     t      o              X                  4,     p        [      x H      (t z X   j   H,       \                                                  d                     d  e  h                  s  X} d7     <  $  x , z                     H             7         L     0I d D [ `R      |k      ,   dv \s ]  <j     /        d                                                 d                 <* d } 0 d                 @&  ,*      + D*           p                     <         |)     , X                       L p~   u     k   \X Q ( . 6     <0           0-  H x                                                   d              v X     R                                  %         H                                            ,                             8V @5                     ({  	 } F ]      P                                                                               d         d     $ z ̼                 p                              e                      0                                                     t 4  4 V y                     g  i   D              +                                                                         d     d  $     
                 p d      p. `         x dM          Ԇ | $              /                         (N     D ,R                 hX  D      D< 8  + * I \         < l1         U                                                                 d     4         -                     z             |          h         ds                                                      L a , Pl                 <             ,S   L  X TZ F             (                                                                                                     d                                                                                                                                  @) 4-                                          | o DF                                                                                   n                                 |3                     T                               	   |f                                     e                L?                                     ;J             '                                         my              W                    Z                                                                           +J                i                 0                                                   FL                 /                     nW                     2                                 ō                    	t                 @                    k1                -Y                                  m?                v               C                y                !           P   d     8  < - t_     a z                  t s  ) 8 v  a   )   TC  <E           |          * d(     T 0    -  `u ( 0    T ,          L @ H   (            ,d          d    P    T     , T                  P     HM X      h   8 4  X( Lt  < @ 8 + t L  4I  Ȥ ` h |) T* 4 $d  /  8  $  \      p* Df      H0   g  s  (  Q                          p                  0             ' T  h0          4   /  $             چ              Q
                         C     C       \ 8         ^                                  չ                 v5                                     K                 (                                7                 =                
                H                                      
J                0                         P        t   . } 0 lI  W  8 `z                  s  c F  q n ~     k Hs       f 1  I       `9 F         ,H      ( ̧  ,  M m ,     (  ` y t ( * t     H U Y 8O    | <            ,d           dA     D      ( 
 &  k                         T m i  k   ?       X  { + \  l \f F l (} h       h  d X F D L{     I    h     2 | Pg   h 8U $ T             Y             |s     !                \                 pJ          P       d      h( O  z   ܆ t ܣ lG Tt                 )   2 ((   z   0 d x l   p3 X \     P h \  p 4V      l{ t+ ) d hV   pr X ( x p 8 P2 /  / 3     t q q l D L d~ k          `X D      d h ( d   < T/   u                   l     p 	 $ 4 L s `  , 0  ~ T    +  $ X l X  HX l h  $2    < / G H{ 0 Ԛ /  [   d     Q  Ć   X   h                          P                                       8 
     H5 " 0   j p\	                 r?                                D             #                 3                    s                                     C_                    H             '          $    A                 5                @                     (                                  %5                                     J                                 8L                                  0                                     by                                          w                    j                                      `5                                       J                                                    K                           P   d     t   . } 0 lI  W  8 `z                  s  c F  q n ~     k Hs       f 1  I       `9 F         ,H      ( ̧  ,  M m ,     (  ` y t ( * t     H U Y 8O    | <            ,d          d dA     D      ( 
 &  k                         T m i  k   ?       X  { + \  l \f F l (} h       h  d X F D L{     I    h     2 | Pg   h 8U $ T             Y             |s   X         P                                                                                                                                                                                                                                                                                                                                    ˸@ (     
   P      Lz                                                                         t                         d +             \                               `                                       0         X                  W p F             Te                h      D} 8     Lz                             u s 0 H{ d                 F g  X{     {         T      Q     `l )         (v + h <                     h 8     /   }      g        a  . 6 } j 0          ( t                                                  Lz                         d ,  \{                  8n   9 X     `p U  d 
     t      o              X                  4,     p        [      x H      (t z X   j   H,       \                                                  Lz                     d  e  h                  s  X} d7     <  $  x , z                     H             7         L     0I d D [ `R      |k      ,   dv \s ]  <j     /        d                                                 Lz                 <* d } 0 d                 @&  ,*      + D*           p                     <         |)     , X                       L p~   u     k   \X Q ( . 6     <0           0-  H x                                                   Lz              v X     R                                  %         H                                            ,                             8V @5                     ({  	 } F ]      P                                                                               Lz         d     $ z ̼                 p                              e                      0                                                     t 4  4 V y                     g  i   D              +                                                                         Lz     d  $     
                 p d      p. `         x dM          Ԇ | $              /                         (N     D ,R                 hX  D      D< 8  + * I \         < l1         U                                                                 Lz     4         -                     z             |          h         ds                                                      L a , Pl                 <             ,S   L  X TZ F             (                                                                                                     Lz                                                                                                                                  @) 4-                                          | o DF                                                                 hijk`                                                  )                 cI                
                 3                   =                 ~                 P9                "                8                                              h                       P                                                                                PX ,F                                     l $                 8 E                             ]                                                                                                                                                                                                                                                                                   X                                                      <[ m                                           ) ]                                                                                                                          8                                  `F $F                             E Pf                 T                                                                           \ L                                                                                                                                                                                                                                                                                                       ( h                                                       ) t                                                                      ` n                             )     8            d         S ԰ h         0p o             ]     W 7                     Xs                 4*  ]  d-        DX                          4p '                                                                       8       ć 4p     (m ( H     p   XF X X             @     )    d) <     | (  @ x <X         ,w      W    ) $      t  (         @         8      lF                                                                                                                                #                                                               ) 8                                               h                                                                                                                                                                       h8                 XG P)                              4                                                                                                                                                                                                    +                 x\                     T             |z T                  h     \8 H  @)         h E         L      ) n )                                     # \      p               f                                                                                  4) ,             <                  (                          E (             $) F                    )                         )             @ t  8          ( (                              	 ]                                                                                                                               Q                  p i     H t           H l         L L      dT p                                      (     p              , L                                                                                                                           L                                                              P                                          " P         4 4                                                                                                                                                             (u                X#             / X ԗ         ( g         ܋          $u         ر          `  u P X         u  4 T , X HL                             t H                                                                      X                 p         / 4u                 L                  з                           |L     ` u         Q "         Q ,$  t L                 8 |  u                                                                                                               `                                  X t     t t     З @u   t        B $  ` 4j  Pu L  $       t xu XL        4               H t         L f         ( pL P                                                                              `u D $     , d      0      t     <u         8           @       t h x @                                             4 Lu X     u l p             (         \     d                                                                                       p          h                   `                                                 l                           `          D                                                                                                                                                                               $                     ( t                 ,                                                       T          8     x) T                 Q $                                                 
                     ]    (˸          hu                  <              P   u        l   d    	    S	 ˸x            $           	 	                p 	    V	4!	           lu $    a        	 	   U	             $     T          !	          ,         $    @          !	U	T  Ȧ      !	!	h  ˸            |             @                 8!	     	              $   U       8!	!	                  $     "         !	        !	    x|
	R	0                 D                X  D         !	l  H! 	                    #		               "	                `"	"	                  $     `          #	     ˸            $               0#	ܺ 	4             H              #	\  $	          p         #	%	                           @      d               #	                   $              #	 	                          	$   	     l 8  X$	    '	   L                 `  @        4 t          	$	                  $     N         h%	    ˸            $              $	h 	                h%	    +	            $    (          h%	`	<            v P             %	d  HW	           x  P        U     	    | 	     (	    ˸         x%	%	  ˸         %	    HW	&	          4 $   %       x%	&	            ,  %	    HW	$	@          @ $ T  V       x%	h&	h                |  $     O         &	     u   h&	    $	˸                                   d         x%	   	             h        X     x%	     	   0          '	$	D                 X          @    l  D               '	                   $              <  x%	   	                     (	)	˸
    $˸$                              @      .       P      $	t*	`      	ʸp                    	                           @       ܦ        '	(	                                                          	             0     ` 	   @           P     (	P-	`            p                                          	           t      \             	                  p             p-	 ˸        L       [       0     0 	   @        t P     ]       `     e	˸p        L      /            )	x*	                X*	P-	                 $         x*	*	                 x*	*	                       0     +	L,	@      	   P        `     ( 	   p              M            *	 ˸              Y             	      +	 ,	                                                       P,	ʸ0             @      	   P        `      	   p      	0                   '	)	                	      P,	,	                  *	˸     ,	,	                  $          ,	 -	0            @     $    P     "   L   `     0 	   p               	         	                   (	
	        
                   	                 -	-	                 p-	 .	0                    2	ʸr    (     t H  	  l  \ T   	 P 
  0  @  $
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 H
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  8 
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  @ Ј ,  x 
        d 0     
   0        t          \ ( |   p   ܉ @ X    t P   h ؉    p    h H  < P 4   p  ` \ X    x         , h   4
 	 	 
 H	 X @	 
    	    	 (
 
 p ,     	 ` \  0 	 t	   l    <
 (	  h d	  p
 l	  T  $ 	 	   X D	 	   L	  (  , P          P   0    ` x    
 7	  v      T   	  ( ,  Ъ     Q     6 47   X	   l  |          d Q d   u L u 4     (       H 8  ,6  8 X6 6 6 \6 8 (6 H6 6 6  6  5 5 5  p5 5 5 h5 5 |5 5 \5 4 h <5 X5 ܡ L  8   \    ,     H `      , l l      l                                  @        `                                       0                                             dT                                  <        0 \         '                                  <         (         L                                  (        x 4         r                                          H                 R                r                       B                                  <         \0         s                                  <                            -s        r      1 -  s        r                                  (                                            /     r     p0                                                           #s                                r                    r                                  <                   s                                  <        D0          gr        s      P $˸                                          (        h /                                  /     r                1s                                         D          Qr     x0         "s               r        r          r                                  <        j 00         r                                  <                  r               $˸r        r                                  (        |l          !                         $          P/                                                            r        r                s        r                                                      <                                                    <                  mr             H/ l0  ˸r                                          (        l x                                   l                     
s                                         <               0         r                        r          r                                  <        , ,         r                                  <        0 t         r             H   ˸r                                          (        f          r                          1     r     h                                                 @k l         r        $                                            '                                  <        @  l         s                                  <          g                 s     T l ˸s        	s                                  (         <         r                         k     r                                                                   r                             r        %          r                                  <        0                                            <        k tu         ]             k p ˸                                          (        ,l pk                                       r                                                                                         r        r                                                      <        8v T         	                                  <        l          r        r     $l X ˸        @                                  (         Xl                                  D         k                                                  < +                D                                                                              <                                                    <         d         r        r     k @l ˸                                          (                  r                         h     
               r                                         T/ <l              x/         ~r            0                    P   <1       n                                  (                  Nb                                         0                                                                                                                                         <        0                                            <         D                 ;      h  ˸                                          (        0 4                 D                        P                   ,     x +                                                               }                                          <        d                                            <         x                 0      ˸                                          (                                           r                                                 0 $         8     k                        s          r                                          <                  0                                 <                        d0                                               (        X (/                                  |     s            ʸ                         1                                              /  0                       %        p                                  <         L                                           <        |           "     h/ 	 u                                           (        0 /                                                  ,0 0                                                          0 t0         *                r        	                                          <        1 0                                           <        80                       / H ˸s        E                                  (         0 0         s                                         0 0         r                         `                              0     Ks                                         6        9                          $            h                m                                  <      $ D                                  $     $     ` H                                u   \     \ r   r   a <                                                                                                       G  
                D                          @                          x ȵ                                                                                   =s  
                                                                                                                    
                                                                                K                                       r                                      a                                                            7                     S                                                                                   c                                            
                                            Q                                                      /                                  [                                  4                     	                    Y                     C              b                     w                    u                                                                                                                                                                                                                                                                                                                 |  
                                                                                    $     $                               >                    J                     '                                          &                                                       <                                                       \                    l                                                                                                 2                 \ B  
            
     ,                 ]                 b                                                                                   Xb                                         i                     }                     !                    f                                                                                y                 _                 ^                                         T                                          7                  :                                      F                                                                                  K              g                   
                	   e                     ;                                                               E                                     9                     P                                           b                                                                                                     R                                      L                     k                     t                                          Ab                 ^                            V                                                                                      `                                      H                                  	                  a                               o                 6                 X                  s                                                          d  
               l     #                     =                  ?                  W                                       {                  W                                                                            3                                                           j                 ~                     (                                          1                 v                 N                  z                                   q                 }                  Z                                  [b                                      ?b                                                                         b                                                                      	                                        \                                   }                                  	                                      p                                                      S}                 `
                                    
                                                     eb                 	                                       x mb  
                                                                        }                                                              }                  }                     zb                                     r                                                                                                                                    ݽ              g                                                        C~                                                                                                     ^}                                                                                                                                      <b                     ob                    }                     k}                 ~                 u                                  ,                  t `b                 X ~b                 	 }                  {b                 p }                  }                 l u                 \ }                  p}                 	                   Wb                  Jb                 	                  T	                  ,	 ts                 	                  	 C}                  }                 
 wb                  	 Pb                 	 Vb                 
 fb                 , )~                  b                 H
 ]b                  b                 
                  
 b                 @ Zb                 ,
 vb                                    gb                  }                 ` \b                                                                    ^b                                                                                                                                                                            a                 Cb                                                                                                     ;b                                                            Mb                     4b                                                                                                                       o}                                                          P}                     ab                  b                     l                  a                                                                                                     `}                     Y}                     a                     {}                                          n}                                                               s                                                                       _        a                 }                     b                  }                 \ }                 }                 (	 }                     ~              Ċ a                  d}                 u                 	 [}                 @	 }              p                  u                  Ps                  `s              `
 ~                 ~                 x}                     u                 u                     O}                  2b                     }              x ~                                   Ľ                 u                     ~                     }                  }               i}                     l              x u              0                       ~                 }}                 u}                 X }                 h t}                  }                  }              x >            H f     0   ȱ     g        	     h             i     0   7     j                           }                     y}                     fs                     a                                          R}                     nb                     Ob                     T}                     M}                     }                     >b                     u                     ys                     X}                     b                     b                     u                     =b                     b                     }                     b                     b                     z}                     }                     os                     q}                     hb                     u                     b                     b                  b                  r}                     a                 :b                                   a}                     ~                     is                 I                                   }                     a                  b                 e}                 Ga                     m}                 l                     }                 }                  Ub                  }                 Q}                  n                     ~                 b                 \}                 }                  J}                                          3b                  g}                                      Ib                     v}                  }                 ~                  K                      (     t H  	  l  \ T   	 P 
  0  @  $
 $  Ȉ  <  8 ( (   t 4 
    @ x	  
 <     l   
  ` |  h   
    P	  	 l p p  t 	        X/     x 0	  @
   $   	  	 ̈   L (  d D
 p P P 
 @    D  
  
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   ,  D p &   \   	    |	   ԇ 	     d      ,	        |
 \	  	 L 	 	 	  
 `
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 
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  	 	 
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   , 0 t D  l
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  x  \
 H
     
 
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  
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 
   
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  
 
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 @      x    ,
  8 
  
 l 4   @ L $ 
  
  @ Ј ,  x 
        d 0     
   0        t          \ ( |   p   ܉ @ X    t P   h ؉    p    h H  < P 4   p  ` \ X    x         , h   4
 	 	 
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    	    	 (
 
 p ,     	 ` \  0 	 t	   l    <
 (	  h d	  p
 l	  T  $ 	 	   X D	 	   L	  (  , P          P   0    ` x    
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   *            x	PV
	ʸ}        l                 }                 
~              l                                    <        t `                                           <        T          n                                  (                  > ,   
               3                   (           $          |1                                     5  t        #     ܝ      
                                   z                                  <        p                                            <        Ժ غ                                           <                          PH	                                                             (        L           m                                  @       l                                            @       |                                   X                                       @         x                                                                 <                            2         *                                                                                                                                                                                  {        `                ~        U                                  @                          2                                  @        X                                           <                  j        X                                  <        $               p   < 	              4                                  <                                                    (        8          m  .      \ h  < $   P @  ȿ  \   , T h Ĺ 4 , ȸ l T d X  @ u Ħ 8 ԥ   d k u \                   ` -#       v                                                      *           I}    #      $   "   %   !   &       '      (      )      *      +      ,      -      .      /      0      1      2      3      4      5   6   7      8      9      :      ;      <      =      >      ?      @      A   !   B   
   C      D      E      F   	   G      H      I      J      K      L      M      N      O      P      Q      R      S      T      U   "   V      W      X      Y      Z      [   \   ]      ^      _      `      a      b      c      d       e      f   
   g   	   h      i      j      k      l      m      n      o      n      m      l      k      j      i      h   	   g   
   f      e       d      c      b      a      `      _      ^      ]   \   [      Z      Y      X      W      V   "   U      T      S      R      Q      P      O      N      M      L      K      J      I      H      G   	   F      E      D      C   
   B   !   A      @      ?      >      =      <      ;      :      9      8      7   6   5      4      3      2      1      0      /      .      -      ,      +      *      )      (      '       &   !   %   "   $      #   $   %   &   '   (   )   *   +   ,   -   .   /   0   1   2   3   4   5   6   7   8   9   :   ;   <   =   >   ?   @   A   B   C   D   E   F   G   H   I   J   K   L   M   N   O   P   Q   R   S   T   U   V   W   X   Y   Z   [   \   ]   ^   _   `   a   b   c   d   e   f   g   h   i   j   k   l   m   n   o   n   m   l   k   j   i   h   g   f   e   d   c   b   a   `   _   ^   ]   \   [   Z   Y   X   W   V   U   T   S   R   Q   P   O   N   M   L   K   J   I   H   G   F   E   D   C   B   A   @   ?   >   =   <   ;   :   9   8   7   6   5   4   3   2   1   0   /   .   -   ,   +   *   )   (   '   &   %   $   p   q   p   r   p   q   r   p       2                                                                   (        0           )                        8                   Y                                                   r                                  <        D u                 %1                                 <         $1         j/                                 (                  Q                             r     De                                                                                              <        0                                                    <         P         %                                  (                                          k          T         A/                                         ̽                                           <                  r        C/                                 <         p                                           (        1 (                                 	      L                r                                         `0 tl                                           <        ` 8u         r                                          <        X0 (1         r                                  (                                                s                °            ^r     0 Q    r                                                      %s                                  <        L `                                           (        k                                                    @                                                  <                  L1                       0       	        w                                  <        T          |                                  <         0                 		  
                        L                                                        ^ 
                           L                 
                  -                b  
                       3                 /                                                    q                                          )  
                                                                    b}                 a                     b  
                                                               
                                        "                 
                 yb  2         *                                                   &                                                     8                                                                      ?                    L                > 
                L 	W                    2 2         *   t         ` $                                                             h h                                                                                     P XD                                                                                     P 
                X	ʸ 2         *    	                 H H	                          d                                        6                            8      t     Q                       BG                        V     =G                 T                     *                                                                   <        8                                            (                  ,     (                                       (                                  (         H         M                                  @       ȹ ,                 YG                 u                     t@                f@                                      @                    @                 @ 
                       @             s)                m@                    y@             |@                    @ 
                        q                                                            
                       ? 2         *           t                         @	 tb         4                     ) 87     0 l                                             , (                  X                                              +   )                              9         > 2         *                                                                                                           <                                                                  >                          "         H f     0   ȱ     g        	     h        T     i     0   7     j        $                 >                                 I                                  <        , ܸ              и $                             >  2         *   P	                                                #                 | "         K                                                                                     > 2         *                                                                                                                                `                                             > 2         *                           ;                                                                                             :                                                     1 2         *                                                                                                                                                                              * 2         *                                                                                                                             T                                       W  > 2         *                 l0                                                                                                                                                      	4 
                  @                    >                                     * 2         *   @o                                                      x                                                                                                                  w? 2         *   P	                                                                     ;                                                                                                 s 2         *   	                                                w         $      +     x $                                                                                     @                                      ~                   r                                          0                                                                                         81            
    (                         A                         ?                 d                            > 2         *                                                                                                   (;                                                                          D9 
                    b	f  
                                           cD                    8 2         *           (                         ` 
                                 x X     @                                                  d                             `                         V                          J                  -                  |                                                    <        l                                                    (                          8                  p                                   H                H                                     1G 
                                                                                            ~
                                @G                    db                          7G                 HG                                   
                       hD                 bD                    ?                zD                                             l                   / .   #                                     $   &   '   (   *                      	   
                     +            ,      -   .   /      0      2    \' \    *   *   $             (	ʸ      Hh @ 9        q     a        2       t                  $ *   *           t7         u                   $                        *                             0                    x                                  (                  q                                  @                                 i 2         *   	                                                                                                   b                                                       mD                            ʸ                    .                     -G                 N                     ? 2         *   \C	                             T p                                 @ p                                                                                                     > 2         *                                                                                         x	 (                             `0  ;                                  ? 2         *                                                                                                                                                                       }? 2         *                        - L d                                                                   P                                                           4   	(   t d   	0   ( d      $     ~		                  $                    6	                            $                                                         r                                  <         8                                           <        T                          J               ^                                       @       ĵ &                          2         *   O                                                                                                                                                                        (	                                  (                  X                     s  B   ,                                  ,                #                           ,                                                                                                                                    
      ,                > 2         *                                                                                                X                                                                     Q      ع                     *           4@             2                ~ 
               x   V                                     _              T             !                       2                      
          h             ]                U                   2                                      OJ                    2                                       ^"                2             [ W                i                  33          
         j                                                            H 5                                 <j 0                                                         Ё           
   3          
   [L                 x 2                    3                2                   RK                 Z                s                   m                                 l                    2                )                   =J             (	Y                   i              2             4                 G 
                        h                 	i                                                    jy           
   t           
      ,#                       +/                	o                 ,                                     *                 %#                =                 S                 *K                Lm                 !                                                     ] |                 Γ              d	G                                  S                  ?                 		t                 e
             c                X                2                    )             '  X
 
     {                    }                                       2              z                         T                 X	|                                                      %                                  E                              /                                                  4k                          *V                 L                 X                                   P   X                 ] Q                                                       
               m l     [                                      ݓ                 ` ]                                      p                 	                                 J                  P      5  t        K                                EJ                   2                9                q                 h                S                m }                     "                 >                                                                                        8	aJ                w                     h                     x                                                                      2                   M=                VJ                 p                                                                  (       I                                      ] d                                      .3                                     m                     
               D  	                                  k                 *                                                          KJ             	&3                	3                                                       j                                    F5                                    K                  J                z  
                     O3               X         P                                                                                                                                                                                                                                                                                                                                      7	4                                                      L           
      Av           
      ֞                 I                 1                 )3                2                                45                                 u                                  s                 2                 5                {                                                   6J                   L9                 ֑              )                   x       ?                                                   (                                 O9                3                                 I              /             H                     w                 X                  J       t           @ 4b $ P      P lk      k u                   $                           X                                                                     <        X s                     ʸ                u                     N                                 o                 aY                 r                     8                                                                   A                $y           
      g        t           $  $ P       u \     ) u                   $                           ۞               t  
                      i  
                ( $	}                 }5             M              Y                 4                 3                          $ 3                                 <         i         !                                 %                 0 
                          )    (  ʸ0 T                            [=                J                ^                 n"                t                 !k                    >x                                  x                 |a                 #J             f                                       Xw         J                                 .#                ZJ                0                L
                Ձ           
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       .t              p        2                 A                 8                                                                       _ 
                       UJ                5                   T                               	   
                           {                 J        t           } D $ P   
    ] Ȇ }      u                   $                        
           g                                 CJ                             ' 7  \]     J                     t                     }                                                                     i         $ 9s                     Ws                                  B           
                                         q                  %i  
                                         0                s             r                                      2                    J                 Hs                 c3                 	                 ?  
                       9         ' =                  
                      '3                 0                #  
               0*     4           V9                e           
      V                              j                o              j                                                    }  
                h                                     <                          C9                                                 G                    u                 n2                                                  aW                     x                 Y9                                  F                 Pi                 l                             
   ;                     $                  2                =I                  Շ           
   Ky           
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      93                BJ                    4                 S                             l                 1                C                   Y                                                                 $ 4       /                                      J                    lJ                    !2                 {J                   
          gC                73 
                    F	A  
               `-    F	             F	                     
                   ;o                                 *                                ˸~            D 3                        $     c             d     0   ԟ     e                  v  
      ,                                         x                    y        h                    0                                      [                            ޗ     T+ p                                                                    M                              i                4                                     Fy                                                     <        x h                                                   z         z                                  <        l                      `                !   0                                                   PH	x                                  D          h            03                                 <                                k  
                                )       w'                                  *   *    8         V     D 2   4	2                <       ^         O                 L	+                                       0 \ .          
        C                        h             ݗ           
      $                                                                 ,           f                        ,                                               <        Զ                                            (         P                 s/               {                                  <         P                  ʸ0J                \                              h     p)                     -   `                                  %                                                         0    B      >                      x     ~              ~J                                        ]                         T                                             	 %                 K        1           9 Z                                  (         x                                        >              4               t  
                                                      @       p h                                           <        | )                 0               [                                  (        H T                  D  
                    JJ                                                  <        8                            	                            
                <                                    &                     q                                  I                                          
                                                                                                        f                      
                                                         p  ?                rK                     r                 \!  :s                     x?                 a  
                           >                 ʎ                                      ?                    D                   WD                 > 
                       X                                                          ^D                    ?                VD                                     =  
                       y? 2         *    	                 Ī                                                                                                             C 7                     *                 xs                     u?                 ? 
               02     ~                     k                 9                   8                                0 
                       ?                R                j?                aD                                    
                           lD                 ?                K                   
               (     t?                }D                ]D                 y                    ?                X                   3X                  ^	            j                                           @       8                                             <         u                                           <         v d                 ԥ                                                              (        h Ԧ                                            ȥ %                                                                                       <         (                                                   <        ` 4                                           <        @ u         f             4  ˸                                          (        H H                                           @       Ȧ          r                                                                                @        ا                                      [                            
                         2        V          W          X          Y          Z          0         L     ]          3          _          `             b          c          d          e          f          g      +   =          i           j   !       k   "   ,   A          m   $   -   C      .   D      /   E          q   (   0   G          H   	       I   
      Pd	    K                     #           O      b	    Q          R          S      ˸       U          h          l   #       n   %       o   &       p   '       r   )   2   `e	h	                               `  
               D         ? 
                        v v      T   	  ( ,  Ъ     Q     6 47   X	   l  |          d Q d   u L u 4     (       H 8  ,6  8 X6 6 6 \6 8 (6 H6 6 6  6  5 5 5  p5 5 5 h5 5 |5 5 \5 4 h <5 X5 ܡ L  8   \    ,     H `      , l l                                      <        k dU              D p     r                                  (        0                                   4l     y     | %       r                                  @                 [y                                       %               W                                  <         lu                                           <        ħ u         c        	      \u             :u                                  (        $                                        l                                                  @        l              ܧ         w                           	   %                                       <         @                                           <                           Z     0k  ˸                                          (        hu 8                                           @       L u                     b             %                                                         <        u          r                                  <                          h     l  ˸                                          (        u `                         F     F              AR                     % 
                ʸo        V	o     k 0 PP         t           l H $ *   *           t     d u                   $                        *                                   *                @  a=             	z?                l	                  .                    ȇ                    ps  l      
   
         O  p d  7 E X    F  v  ()   \ DR k     C   s <L  ( d{ g      N $Q @ , | D  @ F L   8 @  f + % \ 0'  $ D ` ,< 7 ` 5 <4 X c     % x / `  @ <)   t  p )     @  W D     (     x  t v        \     Sf                 ;5                 8                 I                                  ,                 J                 5       4               4      P           *                                        `          j2                                 <        l (         q5    
              r                                             0                           ˸4               )               C                   
                                           ?                *                    ~?                |?                ؉	? 
                                        a  
                        
               zo    ʸ "      0                      <              0 *   *       @W+   3   *   1   Ӣ P                                     ?                 b  
        @       	     2   4	:                                        R        rl  "      0                      <              ,C    r       @W      r      uK                                      ː              Q   U   W   Y   ]   e   m   q   s   u   y   {   }                                               "   $   &   (   +   ,   -   .   /   0   1   2   3   4   5   6   7   8   9   :   ;   <   =   >   ?   @   A   B   C   D   E   F   G   H   I   J   K   L   M   N   O   P      R   S   T      V      X      Z   [   \      ^   _   `   a   b   c   d      f   g   h   i   j   k   l      n   o   p      r      t      v   w                               	                                   
                                           !                                                   <                           ʸi	LV
	      P     }                                  (        t 0         u                                  @       h L                                     	                         ܥ     t               ~                                                    <         t                                           <        ܺ               d  h	                                          (        T               (                                                    k        l                                                                                                 <        Х                                            <         x                 v     к  ˸        w                                  (        إ P              4                     *                                             @       u $         {                                               n                                  <         Ч                                           <        l               ܦ                                                (         ئ                         b	Y                                                      p                                                                                                                                  
                                                                                                                                                                                                            "                 $                  &  !                       )  "       *  #       +  $       ,  %       -  &       .  '      /  (       0  )       1  *       2  +       3  ,       4  -      5  .       6  /       7  0       8  1       9  2       :  3       ;  4       <  5       =  6       >  7       ?  8       @  9       A  :       B  ;       C  <       D  =       E  >      F  ?      G  @      H  A       I  B       J  C       K  D       L  E       M  F       N  G                P  I       Q  J       R  K                T  M                V  O                X  Q       Y  R       Z  S                \  U       ]  V       ^  W       _  X       `  Y       a  Z       b  [                d  ]       e  ^       f  _       g  `       h  a       i  b       j  c         	       l  e       m  f       n  g         
       p  i                r  k                t  m       u  n                                                                                                   O  H       S  L       U  N       W  P       [  T       c  \       k  d       o  h       q  j       s  l         o         p         q                                                                                                           9    "f592"; 92);  
   qEigenform(D592[2],400); #	7                    W        '                      u                  \             ˸
                               u                  *         2    ʸ                 '    ˸0        R    ʸ        0 (   	               J                  P      5  t        K            L     D)     I            9  u   * ' 8  #  01 4F 5                                 1    ʸ>    ʸJ X         P       d s  R g   h      j h)                    f V \  Ln LV ̦   7 0)          , s s  c * \ t8 c b c U         (   pf  <  X h   . U $R  d     i HV  c <i 8k 8F j  d    ,     k G * UVWX                      u                 L, 7         2                      u                 t          J      ˸P5                5                      u                            R                       u                 H 7         &5    ˸Ç              ʸ     GV                       u                 + @         `=    <˸2        R?                      u                           0    <˸        j                       u                  j         5    <˸3        e5                      u                            f     ˸.              ˸Y:                                       u                           	3                               u                  $         Z     <˸         _                       u                 h 8         Y5    <˸y                                u                 d T         4V     ˸         a     ˸         3    ʸ2                               u                  \         \                      u                 [ d         >    <˸0                               u                           W    <˸         [K                      u                 \	              <˸        2                      u                 ds b              <˸                               u                 | b         ml     ʸ   0                              u                           5    ʸ                      u                 X /                                u                 d          *5                      u                 | (              <˸\         Z3                      u                 Lj p}         0    <˸a?                               u                 `          &     <˸(                              u                  p         '    <˸4        *J                      u                 (          ɿ     <˸5                               u                 $ 0              ˸@        t                       u                  p         h    ˸Z         XJ    ʸ2        0                                u                           s     <˸4        `2                      u                 ̹          -y     <˸S
        |                       u                  L)         {     <˸3                               u                  \         l    <˸k        9                       u                 e U         tr     <˸9                               u                                8˸_?                               u                  |         l     8˸         ks                       u                 }          ,u     8˸3        3                       u                                ˸r         g                       u                 0          }     ˸y                                u                 | i         f     ʸa                       u                 e h}         k                       u                 `)          p     8˸        4                      u                  <         m     8˸        )                       u                 `          nd     8˸J        r                       u                  x(              8˸         >                      u                           rU     8˸{e                                u                 U          8     8˸a                                u                           .     8˸E                                 u                                8˸ L         r                       u                 j  0              8˸A         /                       u                 f          9     8˸         `                       u                  ȷ              8˸r         %                       u                 L          '                                             u                  t              ˸|                                u                 8t          ?     ˸l              ˸ڳ                 "                                u                  X         L}     8˸n                                u                 0 i         r     8˸F         7r                       u                 P               8˸                                u                           0     8˸&                                u                 X          j     8˸         7                       u                 i X         \     8˸l         Q                       u                 pu i         5     8˸A         r                       u                 t Y         4     8˸/         _                       u                  X              8˸                                u                  Tj         E     8˸^         
b                       u                  x              8˸                                u                 ܗ @{         q     8˸                               u                 ĥ R              8˸                               u                  (         m    8˸         W}                       u                 5               8˸n                                u                  Q         ^K T     L tj   H Y H    `t ~ j L p  l-  tv |   h r `p ( F |s   T ,P      t   ȯ   i            t ܷ    X D H |  ( , t ,n \  hn # Q   X j ( (     |                       u                           3                       u                 <p h              8˸~         (                       u                 x          K     8˸\
        3                       u                 ,u p)              8˸                                u                 L               8˸}         5                       u                            Ã     8˸y         <                       u                  )         ' P                  3                   P                                 $                    <     )          -  t   4     +  t   4     #     \     ,  t         4          $  w     %  t   \     *  t                   1     ĝ     r X         P       0 @      4{ [ t dp     P* P ) \ T 4         *     T       R       X | *  xs   f   P P         t } 4 ] dP 4      Lw DW  p L  )             )  X      (V g  
            (U  8*       
            N   ;o    D                  &n                    u                  u                     E                               փ                                        
                                                s? X         P   T*	n t-       8       P  X  X X2         8 W \  . l 	 \      T C |  p  u lN   O  p / +            db  4      P 8 q  T  ,) (]         @o P n  T g  (F  Q E F ȣ     \ c ? 4m  hW	 X         P   0 F H G F G hJ hI G     LG H F H H lH G     H  H 8I H H F @F I H F TG H F `G G F $H tG G H XH F H 0H     4I  G H G HF dJ F hH H H tb F 8] G G G G  H G dH xH 0J F G  G <H HG |I G F H G     G H |G pH I X	/             ,                    s                                   F                                                          J                 =                  J                  X         P    S        U   *       Ht C Pp 7         З x 4 7 C   j     p `k      j   y j j Xi  P Q p         (b j  W  *      \ (z  D @+ ${ T          Dz   $ 8d t     ܪ ( @ p          | &  P        X         P   t'  < x  \ , ( |     |5  0: X  0(       '  P   l O        8   t  E s 4 \ T ( x          d <     4 8   @  O 8 ,# 4     F    h      \      T( P        
               ;o    =  
                    X1 X         P    	  x     [  0 j     l  t  <          x \) r  j r | .     k      p/ j r Q , P @s  r  $s r         $Y r ķ < p  r     < з  r X   }         { ( <b  K 3     t t  t          6     ˸                 (b  X         P   /   \    V ) 6 t(  lY D \        X ( R    X#   4#  U  hN    (8 x    t  |S     R R S ( 4 _ 4   ( ( H t* lV  P*  TP 8f X  ? Ԙ \     -   ( 4)     & 
   	 ${    5 X         P   l H 1     0X z 4. <     ] t   L $9           l j TX p p- t      4     * \ ^ P p |   X ( g            , h/  D C pZ     $| `4   ,  0          <t C  p $g   d  D      z     H 9  E k     X         P      H  P~    V pE  ~  { f X{ ~ @ $     ~ D{ {  L   0~ { T~ f  @m |/ M } z  3  5  . z {     M   n V <j { De H j  |  |   x~ p DI l[ M { }  \m t~  { ,{ 0 O 4     - ] { ^ n  ˸/ X         P       @  xP  T li P  l \Q   H  |     7 (  t Q N 7 d  lW  h <R |  `e $ |n V  ԣ  ĥ `     ` @Q X <& Q xQ s HN x -  e  ) lt }  D  H    	  8     pN  5 @  DG       4 _ 4 ʸe              : 
               ;o      
            0x   ;o    ~U                     v                  c                     J                    >                 fv                                                                                                               4                                                                      w                  Ct                                                                             >                              d                                                                                      V                    }                               AT                    \                                                   j                                      e0             J                    (                    ץ                                   |                 '                J                 ɞ                     U:                 x                                     j0                    '0                	)             Y                                       *                    7J                5                0                                      (_                  I                 ?                                  zG                 Ŕ                    c X         P   $  L   4 , 8    ̲ ̰  T l Բ      P  4  X     ,   0  (   ܱ  в        ` L ر    İ      | $  ԰  < ܰ       h      @       l     l                   X         P      R D~ s ~ H~  x ,q ~ r Hr } $r r r p     q Xs r $s r 8q u r - ,s r dr lr  p 0r tq  q $p ~  s ~ ~ tx     `s s s d r r } V |r r P~   q r )  s r |q $q s <s q X r r r `~ } q X p Pq     q \r q q q    BS  X         P   	̯ pC | 8l         C  TT   h h{      @   @  X lC Q   C  ` g DT  |  0  h       { t ph C   4C   tC $  H  I B  | د     8h h ̥ p  H h ,~  1        X  (h       ƿ              
   K
                 7|                  
   ]                ?S  X         P      h , I (   T  X  X @ <      @ P     8     $ 0   8   p x  ( 0 T        `_  H p0    D     d  \ 4    xH L   1 t p <H   4 H          P 8  ?)                :                    2                                     K5                 }x                 t1                M                 	                                                   x                                   K                D                >                0                                     J=             (                6                                                     \?             9T                 W                 >             J                ?                    (                /                     \                 !                                                  !                    f0                 4              I                     Ӭ                 x             4                    3                2 
               ;oʸ                                                   4                                0                                   /                s                 m1                                      R                  D                                   j                  C                    f  X         P       v  )  x D1 , |& K 0  ,&   L-      F h l c H    t `* Tv | 0 Ȩ / ,7 Q  0  $t d R S          l `W .   X $v ̿ Э @ | 4) ( 6 H     hv < & l \ @ )  Pv \v <  5 K          X 	K                                                       w                   X         P       '  Ћ  І `  ċ 4   x  Y ` @     X d  4 D       l l    8   t   $          h  D < p \ ԋ Ȇ   @  8    Ȋ  ؋ T  L @ ȋ 0  |   p P     (        [                   
               ;o    R              4                u                                  / X         P   Ȯ	    ̡   ,     d < , ԡ F 0 t     \   L ` d   h   D  H  X ȡ    6 h @      DG T t, Р d2 X   ܠ L 0 ' <   l  0/  ,H    ġ L- 0 T2  4 p  &      | P   T H	( X         P      ] T[ 4 h `   XM ( {  \\ ؊  q      P <p { @{ O  t{  M  8{ @ 0%  X p% m  h|  ܖ ̖ pm D{ 8O      | { <l 4m [  (&  (\ 4 { Z  {    {   Z H Y h 0Z  T\ M   x l      { $ h[       X         P   8R <  dW  ' x> \ } ~ $ 8g T  $ t     `) T I ,W H I 01 I  4P \m  U 3  % I `  W @ T^ U      V { I   H p  8 ^    |E I   }     X j  F &  $ pU  <  3 X%     <    ̘     F              h   6K                                     }                    }                    J                                         hr                                                _r                                                er                                                                  
   rT                 ˳                                                f                                     rr                                                    I                                                   r                    \r              c                                  }                                   r                                  *                  >                    "/                 j                                                      (                                                   >                     <                                  3                  B                                       <                  D                 $                  r                  =                  #                 ]                     1                 O                 {r                     ^              WJ                1                  V                     $                                                  X         P   t    X d     ؞      , 4     ̝ ԝ     4   L  , `   |  ̞  x $  0      D  `    0   ( $   \       @ П  l       ( `      \  T  Ȟ                                5                                  1                                    ׫                    z|                 6                    S              
   A                2                 
   3                               
   j              
   :                                                                     ~l                 W"                 
   '                                f             S              
   k              
   4             
   
                               
      J                  8             
   sx              
   !                           
   +             
                                                                      
   w             
   t                 Ղ                 X                                   J             
                   D             
                    
   =3             
   2s                    M              0                                  
   2                 2                                   0             z                !                               M             
   h                  
   5                 T3                              
   i              &v                            .                       z                              "      S                                 wR                                                      (R                                       UR                V                                      QR                <              &kR                ,                 R                                                  @	              >                                                 :   fR                V                  d"              :   \R                                 (   dR                V                                   H              2<              8                                        {R                                                     .>              "                                  t                2                (                    <  |R                              4                 0"                 &                    R                              ,!                               0              T                                                 vR                z                                                eR                V               (                    $                                  ^                  %              @  iR             
                                                                       "WR                V                                :              0                       R                
                 8                 &              )                 
                               
   sR                V a                 D              V   Q                 
                 L   oR                J              ZB~                                                      \              x#              ^k                  s              T                    6                    T              \L                                     `  p              l  J                  Z  
               -	ty	                 J                    x                                                 x                 v                 P                                  J                I                x                 jx                    %y                 '}              /              
                    x                                  
      U                                                                    F                 x                               9                 &                                                   #y              S                                                    
   a                                  s                                             ~                     x                               ,                 ˈ                 
   &                 z                 px                 
   *              q                     ć                                                    s                     3x                 U  X         P       l D  0  8  8
       Tk ؎  L \     h \  d) PU    d hi l P 8   T t  x[ <l |V 4W $ m o     o p L |   $B l       X V   (V 8       8h 3  8r PV  k  ܌        ܭ D 8&    Ou                 _M                  v                 
   N                  Kv                                    ׹                     ^v                 4                                
                                                   
   x              J                s                                                     1                  1             J1               1                              
  K              
                                        /                 u                  Y              k                 	                                                                                        K                 Q                  i                 5                    X                 _s              [                 S                      g                               (                 7_                                 j                 2                                                    9                                                                                          4J                                         GJ                 s                                     s                                   V                 |k              ;                                                                                     x                                                                                                                                                           t              DJ                                                                                 
   z                                  t                 I                    MJ                                                                 e                                    I                                  l                               T   $   mv                 .y                  ci                                v                                                 U                 b                                        h              "   .                 O                    
                                                                     }U              $   
a                 U              $                        }c              Vy                                   ֢                 5f                               i                                         q                 ]              Y                 e                 0                 w                                   &y                     /                                  [V                     wv                 x                     0                                  b                               y              v                  1y              j                  "                    |              )              
   gy                 ߔ                                                                    Ɣ                               ͇                                         M                                       v                    cv              W                 x                 W                                                                                   {                                                 g                    g              @   hg                 u                                      <t              *                                                                       =              U                 j              w                                             ״                                       cd                                      ՚                               Dt              ,   Ŵ                 s                    v                 m                 k                                                                                    
                   ;o    I              u                 S                  (   Y                 a                 F                                   t                 '                     7                     &                    ܡ                 u[                    v                 c                                  .   T              (   6                 V                 p              Up                 ޖ                               (   2                 *i                     Z              ,                                    %_                                  $   ZZ                 
                                   wk                 !                                   )                                z                                      !             $   |                 F                    ?                                  "t                                   ! X         P   	0 D   , ̣ أ      T  H         ܢ  L   , ` \     ( T X ܤ    4    آ        h      ȣ      L       D   4       ,   h     H @          L  $ @      X         P       4n n n o Tn $n pn o m  o \p  p 4o p p o     o p o n n o 8n dn m Do o xp (p o o o  o o Pn o m n m o         o o Hp o m n  p ln Ln m |p H m n @p o m n <o ho  n n p n n n n ,o  $o     o 0n \o o m ʸ/ X         P   H	T X! $ l%   L =  л    D` ( l     +  4  C  ,    h  $ `   |$ | 0   hT a 4`          X$  \ @ , (  D ` x  `F ` \   x B X x T g  $ `? HF ,     x      `     l K X         P   @	( P  p % ` , 8   H X   $ B       $ ̻ x  8 d  ز    t g    p$ T   |         |  $  l-   ,` (C  #  P  < l$ 4   (%   ػ  E   (,       $ @ # ( ` 	 
               XJ                     "   q/             /             D   p/             kb              "6p X         P   8  l T  @ P   \ d  H D T         h p @  L   x    <    <     L l  ,     H P D , 4 D t @  x  0       `  P  |    8 X $ X         T  H ;	W  X         P   @ x h     $    T  <   \ 8 4     , p  < D    |   ȁ 8 D  , @    L  ԁ H       \  X $   4 Ԁ ́   ( T H t ,  L 0  d d 8 ā   ( d  P      h ܁   <     g              (   B 
               ;o                 #  X         P             < dm  p 0  D П   $     (  L Ȟ      \ ܟ      X  t  HM  L        D | l X 3 p      ԟ 0 x  ȟ   @  ̟ ğ   xM   4 ԝ D |  T     $   h 8  +                `     X         P       D # T         8 4          $    t   8 d   t  X   h <      ,        H L <  p 8  P l  @ (    P   0 T H  x (   \       4  d  l     'k  X         P        d4 + HZ  5 < x&  5 & q d,    ܠ P     ̠ d] : |&    h @ (4 4 3   F  @ 3 Z x? 5 T&  c         ? E   l a a L'  t     ` 0D  $?  dI Z    4[  & L[ < k     @4 3 & G ?                 0                       6                   2                                                0   ,             %             "   &                                 4                                                  N             :                                                                                     4                                    .                                              N                                                                      +                M                                             8   n                             &                                                                                                                                              "   "                                                                                 /                                                                           8                 5             _                                                                                       l                                                                                       :                    	                                                                                                                    Z                                     X         P   & ܼ ȼ Լ     G  Ľ ( Խ  0       l  L    н  3  L   @    Ƚ    ؽ   HH          1 ` | H      4  D 4   x |  ` , ^ D     p <  ( d       L     X         P   q	G @ @V & (H ؽ G   G G G , S  hH      &  H H hY 2 G xH HI   V @ G  $ # R  H pH 8I pV DH     <I p @ G H G t[ G TH V  A d$ ` LH V > ^ н  I A H Ƚ 0 4  G \  8H Y R H     lI I G I H ` B  
                L   ;o    ! X         P    - P- `-   q Q ,- ' Q d. u 8. , L. - (.     0v $  . - 6 \. ؟  ' - D' ' - X D . , r , u ,  H.     , . `. . / - Q p-  u - -  q  Q ' PW p -   h-   % , - -  $  -     0- q $ d t.     #                 p              N   67 X         P      H  0      | x <  H L H        H     , \     @ h | t   4  | 8 h      L  @ X X   |      p    (  ,          p $ X        l   d ~ #                    "                "             "             !             #                 "                   !                !                    !                #             :   !             !                   #                 "                    "                N              (   #                #             "             "                    #             :   "                 !                "             "                     !                "   !             "   #             8   "                	#                   "                 $   "             +              <   "                 "                "             "             4      "                   "                 "             "   "                "                "                   
#             I                   "             "                 "                   "                "             "                "                 !                 "                "                    "             G                "                 "                    "             "             "   !                "             $   "             >   "             "   "             "             "   "                   "                k                     "                "                 "                "                           .                 0              x   6                                  ~                                                            8              ~.                                     G              "                 v                                                                                              .              D                 |                 "              \                                  *              ^B                 >$              ^*                               x  \                               F                               ,                    "              HR                V               &                 \                 (             (             *   $   S)                 (             &   (             (                )                a)             ,   )             N   (                &   (             N   (             (   %   (             (             $   8)             (   A)             (   (                (                 (                 &   +)                 (             &   )                G)             (   (                 (             (             (                (             *   (                    )                &   (                 (   (             (   (                L   )             (             )                "   (             (   )             &   U)                $   (             (             :   
)                ')             &   "   ()             (   -)             &   ))             (   @)             R   )             &   :)             !)             "   Z)                (                 7)             T   (             0                 *   V)                b)             /)             (   C)             M)             #   )             $   (   $)             (   )             0   Q)                 (             (   )                 &   =)                (             (             (   &   (             r/             |/                 /                 /             "                     v/             "   k/             a/                 D   g/             H   K/                 u/                 $   H/                "   `/                 T                   L/                 h/                J/                 _/                   x             "   b/             [/             0             1             @   S/                 $   11                               t/             D   ?/                1             "   (1             @   >/                =   c/             f/                                         0             8/             "      P/             5/             $   M1                    D1             "   R1             :1                    A1             J1                    X/                S1             "   M/             "   /                /1                     41             &   61                    Q1                 "1                 1                   1                 "   91                 2/             /                    '1             $   $1             (   0                     1             "   1             "   /             $   B/             7/             %      O1             "   Y/                      1             0   B1             "   >1             "   ;/             0                $   ,  X         P    !   \   !   |!  " p 0 p  @! ! X  T!       H!   l!   ,-     t!  !  ! P  l   " 4      T,  !     L" ! x   $ 8!       ! (      "    !       x  ! "         | $!       X \   |      t                    j             $                    B@                               D   #              NLg                 *              L   H                 X                 0              B   Y              D   %                 8A                 4$              Zh                  07              6J2                 =                 :                       T                    m                                  B                ,              V                 2
                                     >                 R                V                  :                 6                                  <                 I              r   /              J,_              $  @R                                    U              L              N   e                               x
                 J                                                       
                 B                    3                    1                 
   [                 w                 L              F   i                                     FN                                  4]                                  N
                   ^              x   K              D                 f	                 '              8F               bk                 E                 P                :                                                   p                 @b  X         P   $   @ dd ,b x  ? W Dl $l    '  < , ,Y     0, l m (m k l Y  X N  Y x    T p/ Ġ $   <|  ld     ,  H? ] \ lS  i     x  ̸ k P   i X І  I h T, H , Ȱ <7 l       ? (?   c                       0  X         P    ̞ d 4 @ X ` 8 ؟    l l   h     ܞ      Ġ | p  T     `    X   \ ,        4 ̟   0    Ğ   0   $  < H D P x       ؞        x     h   X         P      d  D t 0        $ $  T       4 \  (     L  ,      x Ȑ    h      |  P   p  |   \    x      ( H  l  T   ,  X        @       K             '                "                 (   H                 (   y                 r             z              aK                $   f              $                 .                 K                *   FK             D   1K                          K                   f              (   (   (             <K             *       LK             K             CK             ,                    KK             "      mI                           &   bK                J   TK                jK                 ,   ;K             (                       k             (                 nK             (      uK                           $   \K             *   ZK             ,   hK                             
                T   7I             lK                (                    vK                ~K             *   m             I             (      I             N   K             R   I                    1I                                              ,   XK             (   5K                s             $   (   '             L   I                K             "   K             K             "   K                mK             (   ( 
            H   ;o    E                               I                (                K                           *   K             $   F                *   K                F             6   l  X         P   p )   ~  X) <X ( V @ X TX Q   \X     LX ' '  8 Ю   	  \~ | PX L ,[ x  *  l    p* ,X  Ћ X     x~ ,~ $ 6 P ' p8 HQ   R )  DX k W  l X{ D ` ė @( h( # dR u t
   X*  R     } lW  5 0*    X         P   	 @ k 0  1 j t/ A L E T V F k |2     @ X xA A  j d> |b  % % A $T  > F (H  ^ U @F T 0 1      @  ȳ A 4T  G  0 \i  A | #  D% $ ; 1 tF t> T T T Į  PA lT ` DH 0 P0        > 41 t0                  &   /             0   Y(             (             /                                 ,   /                                        (             "   2   /             
   K             &   (             I             ,   (             P                 (   k(             0   *(             D(             *   SK             .K             4   s(                 *   $m  
            ;o    r(             '             (             2   (             :   R(                             '(                (             L   (             a(             (   (             *   (             '             0   L(                (             *   (             +(             ((             X   8(                    (                ,(             e  
            4      ;o    c(             ,   I   I                 *   ?(                 b(             *   (   4(                (             X   7(                   O(             $   S(             U(                (                   (             0   :(             2   (                    (             (   h(             "      \(                 (             "      d(             (             M(             *   u(             `(             0   /             *       q(             L                         f(                ,K                $    (             G(             T   /(                &   G              *      ڞ                  _}              <   g                            $d                  X         P      \ Z Z @] d\ Z ,[ l] P\ @\ Z 0] \ ] T\ [     l[ [ X[ \ [ [ 4[ ] t\ \ ] \\ \ \ [ L\ \ [ <\ ] p\ h[ 0[  ]     4\ ] [ [  (] [ [ P] [ Z \ X\ `\ (\ \ [ `[ Z x[ \ x\ [ 8\ \ p[ L[ [ Z [ P[ \     Z ] [ |] 4]                   F   * X         P       ^ N < $G 8R x ^ A S \U $Y $^ (F hj T z     ]  HU J D^ t h$ J / ^ A 0k A ^ `Y  A Ă } A  { XJ @ T     I hF j  J PT @J P 4 j <^  R I J x^ A D>  4F J A F z H$  B ^ A XV x} ,q ( {     k j T A xE       X         P         8F $     Q  F  X  t      X T  i l 8  D   ذ S F 0  ̰ а     8      = \ ԰ p   d R       ̯ L L ܰ ,   ,T  x p  $ F <  p ܮ       p P Ԯ   	j                 w              b   ,              x    X         P   } ` Ў ؍ 8  (   h  $ \ ܎   8     <    P Ԍ  4 Ȍ    (  D  p x  ̎  X       \  d l   t   < $ 4  ȍ   ̌    0  4      ؎ 8 L h     8 ܍      |U H  X         P        $  4   d 8 8  ( 0  t h        ` t D    l <   l D T          P (      @  @    d \ T  T   l   L   0   \    H L        `                             X         P   `O	,h W   \i g h h h li h g 4h di  g g     ,g 8X  (h h  i h  g h h LX g  dh  h ,i  h  h X       dg g h g   |i : Li  g   h h g \ <h W d h g Di  X lh h h h | h |     i 4	  4X HW      X         P   Q	    l <    4  P  t       8  \   $   \  0        $    @ x     h     L       t  (      l  @ ( D L L  @              T     nw              6   Ȑ              D   |              2      6                 ׷                                             0                                  0                 6                               4                 'w                 Ww                  *   ۷                               :   (o              <   2              2   }              4                    <                                     ,   4                 $   <   *              f   3              
                 ؏                            2                 .   g                            2   E                  .   o              6                 2                                     j   0                  w              5   Sw              *      -              8   /              \                    2   w              p                            .   [                 5              :   w                                  w                    Gw              H                 \   ط                 Zw              aw                               0   ,                  t              .   ?w              
   7w              (   Jo              *      jX              xw                  ^w              0   n              >   n                  w                               q              
   w                    V              y                 #   	~              <                   4             F                     3              DV              
              :   l              |   }                 }              D                    <   }                  ,              <      "~              :                 H                     }              <      s              @                    }                                                              "                            <                    s}                 CL              <                    |              ,                    ^   ͐              B   )_              >   }                  <                 >      {                                    <                                     ~                 .                            @   :                 t                 $   ҫ                                  :   }              :                    e                  >   ~              >   6   bR              >                                   >   6                    .~              ~                 >                               
   (              ې              @                 @   l                 :                               :   }                 ܐ              >   }                               8   w}              4   ݐ                               J   !                                            >                                 6                6                4                                                4   |                    '             *                "                    4                4                0                d                   <                8                :                @                                             f                                          0   :                4   2                4      n              8   m                 .   ʢ              ;      m                 h                 4   .              
   0   #                 j                 6   /o                 N              p   
m              ʐ              8   s                 2   [              <   ԅ              2                    `w              
   "o                 -              $      -m                                N                 o              
   6   l              l              8   0                 o              ^                 l   n                 4   *m              >   г              Mm                 l                  _              ,                  
              l                 Ro              :   %m                 -o              0              6   (   o              n              *    o              @   l              Kw              0      !m              B   (   m              4   l                  w              4   =              8   l                  4                                     o                 0    m                            ,   l              <   6              l   l              )m              $              .   gw                 m                 J              :   o              4   l                 l              l   sw              hw              0   n              8w              .   X              n                                            j   x             $   :                             :   y             2   `                /                    n             6                4                                   6                                                             &                      
             j   i                             <                             8                
                8                $             n                4                 :   1                          8                                                    r                                                          .                .                                0                N                l                             6                .                 TX4 X         P   4y D D E D E i XE  E $E E @E E E HE F E     pE C D D E DE  D dD HD E D ,D D D LE `E E D E E pD D E D     hE D E hD 8D E D lE E C D E E $D D |E \E E D E E dE DD E D xD D XD |D D C F      D tD C E E  e                 e                 ]  X         P     t z Di <{  X ( t < O z | d $~ @~      l Y { { h   8 h <~ H~ lh p{ `  { 0{ { { p ~ | T| ԥ     ~ ( \ p L \g H F  8/ ~ <| @{ ~ L~ ~  {   f { `   0  ~ p~   ̅ L      h z 4  d , X         P   4 '  ( d( > ( ( HJ L  m lc ( <J \J  ) c @c      c ( 0c b <c p( dn ) N ((  ) b  r T( ) ( ' `b ( q b l b `(     ,( ( tr Hc ) t( $c b b ȡ pc  ( b ( Xn Pc  lb TJ o b Tc ( r  ( ( ) ( d dc 8G     T3 ( ( t' ( { \  X         P    X( P& T $( ) D' '  h' $)  , $ l'  T'     Q X'  \ ,B V ( (  T l( 4( V h(   \R '  8)  ( T(      '  V '   lR | ' ,'  \ V ,( ' < ( V $' X D( ĉ d' ' & ' &  (   l# )     `'    V B                  Xy  X         P   Tm |g T  d xL ," $  L #  l   T ش     h    g 0 Xg <L  8 # p <# f Ȗ 4   # e Lh   g L      \ h  L f l 4  8 d	 w L T9         xg  #  K  w Tg  g   x      . G 0 @L f q   X         P   w	< H]  j i @k i d<  ]  < < k ( j v     \ \ \i \k < < i k  4= dj C ? `= (~ j t l< < Tv 4< < < tZ     < <= < @ 0\  k 0J `k i x< \ = 4j k   \ O     <   [ = i < = i $j  = d j     <  [ i P ˸                 }              >   *              zP              T X         P   y	0| h  { z { { { | { $ ${ {  | l{     ({  L{ l| X{ | d{ d z {   { | P| | { { |  z H z | {     | 4 `{ 8| { { { <6 \{ T| t{ 8 X| { 7 d|  |{ { { T{ {   { z   { @  D| |     { 8{ Q x{ {     [              $   e              M[              "      e              :   e              _              J                 ^                 4   e                 <   ^              HS              :   S              t                 W                 D   ù                    ^              D   @   b              V              e              P   =X                 >   ڹ              x   9   z                 e                 e                               F   &                 e              B   .   Թ              V                 a[              J   ^              B   ^              |   \              Z   _              F   ^              :   r1M              J   e              :   V                  V              h   S              e              H   e              >   e              B   e              8      ^              9              @   ^                 e                 f                 :a              ^              :   ^                 B   e\                 z   e              :   e                  \[              L                 
W              V              B   GW              B      jS              ~L   ^                 W                 @   e              e                    e              B   8   V              e                 +   VS                 8   e              f              @   wV              f                                                    T^              
    Y                                     LZ                 L              
   W              2             $              
                 "                    J                 8   v              \                                   @                   &                                  R                     
                 R              J$              @
   Z              0                                      XW                                  B                                       W              >                   >                                  &                 U                 0                .I              X2                                                  *                                 0e                                   *                   &                 &              (   |                               
                    .[                               24                 .                                                  $                    |                    N                 e                CR              *q              $                    z              !7                                                 $                                     (u                  w                 [              U              H   B                 O                                  2              ^   T              :   ~              vP                                  *   P              >   &              J   -              :   lC              إ                 ZV              t              
   e                                  r                               <      N                            L                               {              @   U                            H                 @   U                 <   L                               
   z                                  4                 6                 <                 N                    <                 
                 B                    F                                  o                 @              
   U                                  !                 @              J   j             j                                    @                  b                       7                               K              v              F                            F                    D   1              F   8                 F                    D   R              p                 @   U              >   "              .                       F   n                 <   r              F   iV                            W              F   2   V              <                 آ              "                 z                                   e                  v                 R                 T                                                   R   X                                                l                                 /,             l                 f                    `   ~T              L,                  X         P   ԫ	p  ؀ Ԁ     l , @ < D         \   1  ` ̂ D h  d    $ X ( X T  ԁ Ȁ        (   ` Ā  ́      0 d $  h  x ā  0    4   < 8      ̀  H                                     L                                  U              T   l                V                             T                   u              d\   N              Ȝ              T   d              H                 _                 T             V               R   B   T                                                                    T                 J   KT                V               T   <                 \                 F                    L   k                   ؜                               V                 B   b              w                               P                    L                    T                V               T   c                  H                    T                                 B                                     a                                  }              P   T                ֜                            Z   >   ]                 T                V ?              
                 tƥ                               J   T                                    K                 H   ,                 T                w                 L   `              0   qT                                 <      p              Ĝ              T   A              V   MT                V               R   U  
               ;o    <              r   ^              L      Ϝ              R   -p                V {              F                                                H   T                   H              P   ɜ              :   `	              L   @                                                   Y      h              m                 I                 k                V p                 r              P   5,             V   s              H   v                 [              B   |                 T                   hK                 Xi                                  @              :   s              k                                 F      ё              D                 @   B   >                 k                   ^                                                   iv              |              P   ov              B      BT              0                    >     
               ;o    x                 @   h              B                 
   U              J   C              J   b                 ~l              H   k                V U              ~x              x                               Mc              =   <                 k                V Z                                     k                {              N                 D   f                 -              D   o                 qi              4   J   qj                              @      }              ]              B   W              8   T                              l                   |                                   {Y              D   XY              N                 2              H   u                 lf              d                    |              T             	   f              T   zk              J                 D   k              :   Bu              l                С              I              *                    jk              p<                 >   H   ѡ                 z              D   k                              |                                H                 D   P              B   y                    >f              Z                 X  X         P   ț	+ l+ |+ + + , `+ t + T, + + + h+ + ,     <, , , + , + , + $+ + + + ,+ + t+ $, + , 0+ \+ L, , + ,     * , `, , , , , *  - , l, X+ * |, P+ * + , , h, + + 0, , 4+ , ,, , D, + (+ *     x+ + <+ , * 8	5  X         P      < \        <             L t        l  (      p 0 \        ġ  0 , $  x      \       ( <    P     p            k                               R   Hu              N   $             v   T                V              j   hT                V              n                   x   h                                   r   3T                V                                        
   dT                                             0                   YT                                           p   |T                                                                           l             t    
               h|    n              J   |              .      s              X                 J   ~                               L                 R                                  >                                j   Xh              bV                               D   T   0              \   /                                                              $                  H                 L   
                 V                 ە                 i              S                                  ^   o                                                @                 l                               Z   kv                            V   ѥ              y                                                F   =              N   tR              P   
   ȥ              T                                                  \                 B                          Pd                  ֥              
                               0                               R                 j                                  H                                     
   h                                                B                    
   ۥ              H   F                                   ^F   d                 C              ^                 p                 J                    t              2   b                 T                                       X         P          X \ D 0 ܅  ؅  `  D      Ȇ d  $   |  l p    (  X L   \  L , @       | 8 4     d    (  D P D   P ̅ Ԇ x `   Ć H p < t      L ܆                    ˜              Z   %l                                                    T   T                              T                    @      4p                ת              R   e                 }e              R   T                   Ȉ              T      "              R   ι              V   T                                 R   b                 q                               c                   3                    T                    È              V                 T                                  X                 L   ^iT                              R   c              x              j                    $              V                 8                                     Pq                 D              
                       J                 P              8
                                 j"                               p                                  X                            $                     }                    O                                  l                 (                                  |              bF              0   0              
                 p  h              p                                 B                    V              Td  O X         P   N	 m m m l m l k xl 8l k pm <l Tl dm k m     0l m Dl l m m l xm  l k l `m k l l Lm l m m l m m @m m     k m ,m l Xm l k l m l \m lm ll m @l Hl l Pl m 0m l l $m k k Tm Hm k k `l l l     m l  m <m l     {  X         P    \    T    t     d  , ( $     d     0 l     L @  |     <  ,  P          $       x   $ 8 l       @    x T   x  p         X h   d  X         P    @w Tx / w 6 $x x @x 8w tx 4w `w 5 6  lx     v w Hx Hw v x 6 Dw |x 6 x  <w ,x pw Xw x `x v w l6 x ě      w v w x w 6 x w ̛ hw Xx w x w w x o Tw hx x w 0x w w 0w w  Dx  x v w w     w w x `v w t               h                 v   T                                 v   y                 ET                                 
   T                                                  T                              `                 
   kT                    ΋              S                            j   V   yT                                 ^                 d   pT             
                    Z                 Z   Fs                                                l                 m              ^                 :                 &   ӟ                 ^   ̢                            j   f   T                V [              ^              t   u                            ~                 .                    l                 p   7              ݹ              j                    f   *M                                                
   T                           Z                    T                ƞ                 l   Y              l   T                   ع                                                           h   ֹ              О                               <      qV              T                Ϟ              
                                                   l   J   ΢                  X                                                      T                V                  י                               k                                 f                 Z                    Q              b                     Z                       ̞              ܞ                 ^              b   ϟ                    T                              RҨ              \   JZe                 a                    L  X         P         H  P \  l ܣ آ    8 p      У     d 0   D  t    p   P    ԣ  $      Т d أ h    d L | Ԣ  8     \  x    \  @  ģ ,       L h   Ȥ     X              p   X                 
R              Z                            <   5T                                 P                 F              LR                V               B>R                                   ^  
            x  ;o    4                  X   S                            `   L   K              ^                 \   Q                    %                            f                 :                    d   l                                                   e   *              X                 l                  Z   Z                 p   
              r   $                                             N   n                 x              Z   Xo              n                 R   :              8                 P      }              [                 I                                     W                               _              b      &                     .                 ?              p                 j   2                 R   r              f                 f                                  d                 >A                 5                  V                 t              r   1              f   h              R                    <                               ^                 0              _b              \                    Y                                             u                 )              6f                 "              f                                         ,                  \                  `   F                  M                            `   s                            /                                     l                                                ՙ                 ψ                 ޙ                 T                                 e                  b                 L                    6                  T                V                  T                V ș              R   F   e                 T                V C              6   [              X                    6              X                        R   *              V   J   r              N   k                               D   Z                  ܪ                               b֙                 T                V &                 ę              VT   T                V K                 &T                V               +                 q                 T                    q                                T                 T   r              b   Ĉ                 J   Y             T   ߙ              f                               X   T                V                  	U                 +                X                 V   kI              4*                              W              b                 ^   N9I                 P              Z   q              Z   ,             :   U              n   r                d             ,             ^   R              j   i              v   M                BU              `   `   @P              n   U              wP                    *                                  Z   +             .j   0             ^  
            
   ;o    N              f   P                 t   )U              ^   i+             8             P   t   ^P              x                                    ,             f   U              +                +             f      Z              n   <U                              QI              `                   :V              {P              x                 d   +             +                 ^                    ,,                              p   S,             fP                 ,                   TP                 1U              p   *                 ,             l   WZ              `                   #,                                                  U              l   ,U              Z              X      ,             l   ,             p                   CP              @      +                   Z                 -                 f   ,P                                                              *]                            W              X                    H   :IV              d                 `   CxP              T                 d_              `   hP              \   XV                 W                 Z              R   >W                 \                    Z                 
   aU              Dp   jP                 X   P                            d   T   dP                 d   }T             	   W                 T   nP                 Z              I                 W              T              b   W                               :   3U              T   W              m      Z              P                    Z   W              HP              r   )  
               ;o    I                 Z              K              $U              cP                 \   >P              p   N                 
   T                 W              6                 j   RU                 X   Z                            h   k              h                                                   j                 V                 f   F                                                f   U              D      x                 W                                              ^              V   `P              d                 .&   t                 U                                     T              
   X   WU                                          v                                                                                           (;                }                    `T                V               ,             +             
   oT                   +             \      gT                                     \T                V               +             +             ,             
   E,             `   tT                V ,                V   -,             f   Z   [T                V T              j   +             q      +             +             cT                V +             n   8,             d   	,                `   +             T   :+                   ,             .   0,             F      +             +                `   bT                V +                j   k                 zT                    +                Z   +                xT                                                                   ^   +             V   +             F,             f   3,             ,             n   ,             *,                 ^   c,             V   +             N,                +             +             d   ,             r   R   y                 ,                *p                V +                <              >    l                ,                k                4,             h   fT                   U              j                    jT                V .,             t   +             +             &*    ,             Z   T                 ?,                T                   6,                            8v                    +             H   2+             P7,             j   L   ,             *T                +                \   T                   ",                              uT                   +                  X         P   | 8 Դ \ H     ܴ Գ  p   4 T      >    0 t    @ X ȴ 4 p   X  ,   d |          , <q  |  P \ H E E     ܳ d 8j      8  Բ     d  x س         L d  4               3             )             n                 ;                5             h                    r                 ʣ              f                                       HT                V D                p                     r                 l                p                       r   К                  p                     (7                q                               x   y              `                 !             
   %                n   ؚ              '                 v                t                     O             v                                                   t   R              (                 r      =                =              t   d                 P   (   .                g   !              
   ך              f   $                               u                                  l   *             n   /             ٣                                  o                              n   M             r   E                r                 t                t   |              X             d                                z                 ף              x                 n   t   Ě                              n   6             p   f   H                W                 h                 t   ݣ              S              w              r   "             v   2              F   x              .                 r9              v                    q              ^   '                 
   b              p                 l   a                k              h      $              ~              z      1              d      =              i   <                 W              z;              t   .D                 z[                                H   f                 U              d   |   {              |   `              xt   J                               |                               }                               ^                                             |   I              r   l   N              t   6                 |                               
   (:              2              P      M              l   g                 U             Y                                                t   A              Q                 
   s                    0                 "              ~                                  x              N                        h                               v   T                   m                               n              v      O                                  tp              r   5                 L                                  |~   u              x!                                  jE              r   X              3                 |,              R                 y                  j              |                 z                x   vT                                      NT                	                             |                                    h                x                ~                |   V                                l                                N   "                                      ~             h                   |	             ~                                                   t                   j                OT                V              z                F   'T                V                                                 j                ZT                V              t   {T                                6                                                                          2                                 l   mT                V |             b                1 
               ;o                                 n   ]T                              b                   :                                          x                   z                             T                V              T                                TT                                           ~                 @  N-             z      ,             z   zc-             ,               ;-             ~O              x   ,             ,             ~|   -                   -                x   ,             ~   .-               x,                 W-             v                    -                 z   i                 ,             |   ?-                |-             z   9-                 F-                z   0-             b   A-                ,                 bY-             -             r                 _-             z   h   X  
            \      ;o    V-                p   b              
   <-                ,                 ,-             N   ,             ~   l   -                p   -             7-                    T                k              x   ,             +-                -                ,                -             |   ?                  t   ,                ,             t   L-                5-             g   -             z      /-             ~   -                8-                 k X         P   T-	T S (T S HS S R T T tS T S @ `S S hS     T S S T S S S S T U <T S 0S hT |T xS  T XS @S T S R T R      T R S DT 4T S T R S |S S <R R T T pS pT tT      S \T S 4S T TS LT T  S S S R XT     S @T T `T S !	j             Z    p4 X         P   3	p x p L  l  `   D     @      ,   \ `      @ d D 0 T    |     D                     t  <   P  (  @ h  ,   \      <  X   t (5	W  X         P   d  X	  D
 	  	 8 	 	 < H
        	 t	 	  P d	 	    0	 0 P	 
 (
 @	  	 	 T l	 $	   	     	 	 X 
  T
 x	 l  	  h 
 0
  	 ( 	 	 4
 ,
 | (	 	 	 	 D	 	 
 	 	  
     p	 	 	  
 4	 ʸS X         P   F  J 4L L L tK K K $L J 4K K L J J tL xL     hJ DK K L LL J K \K K K K dJ K K `K (K K L L K K K K J     J J K lL dL J J K \L K L K L J J L I J J (L hK J J M HL  L K J TL L HK @L     J pL <K L L     	{                CR                   MX              LQ              &  |              2 mY              $|                                   R                               |              N              ` 
                      [              l[             4  $7                V :[             *   a[               a7                V Z             `[                
  ݻ              j  aT                   u                    
               ;o                  xt                               t                                        CT                                                                                        g              p                                     
   f                 
   LT                V                  ?T                                             ~S              $   IT                V               lO                 ɻ                                  ST                }              tǻ                            
   s                                  f^                 f              ~                    h                 xPT                ]              t   P                            j              t                       f`                m                 z                                             t                       :T                 z              v      j                                                   T                                 zh   VT                              v   _T                                 l              ~z   XT                V [                                                z                  `%T                V                                   f~              |   t   ׻                    л              P                       ;T                    ʻ                 v   W                               t                    p                               n   6T                V ƻ              T                                                  p|   ^T                              o                 rĻ                 sT                                 -             |      -                 %-             -                ,             ~m-                v   C-             x   -                ,                t   2-                ,             z   -              r   "-                -                r   ,             >-                                ,                -                M-                \-             z,             ^   *   m              8BR                	                 ~l  X         P       \   \   d L    l   x l        0  | 4     `   P     L  h         L   L , (  p D         8 $ h T `     T \                                 d   D              8                 
                         X         P    | k D4 ' I 6 A 1  I P4 `4 4 d (Y Xu     e k \F  I 4a  l  ! d ' D/   4 h1 e 4f I 0S D' @ L4       ,'  +  I hZ 
  e  pI d S d   6 6 @  t h , 8' 4 3 4 ' I  $ , 4 h     4 h L' 4 '                X   k                                     n                    -                 X
                 i                ݆                  <W                                       2                I                                  W              (      W                                                  g              2                 Cu                 b              Y              
                       '                  8V                 3f              
g                 v                 
                     d                 T   ϡ                                  l                W              
    U                 I                 L                a                                                  Ϫ                 m                 h              8ɥ              &   aI              ,  \U              
      U              "                 c                 
              4  zU                {                 ;              a                 ٕ                 c                 d                                l                 _                 .              $                ^   qU                    VI                                    z                /                              N                 ȧ                    ŧ                 ~                 x(              u                               ~                    BT                                                          @T                ק              $                                     f              X   Y[              ~                                        *  `                 L              d   "   ^S                                                                   |   ]              r                                                                                      ~   7T                 Ƨ              է                                  z                    Vܧ              h                 d                                                       $  b                 Pϧ              ̧                 n              ^              v   S                                 ѧ                 `JT                   RS                 p              ~   =T             	                 rlT                              GT                0              l                 f   	              t                               r              |   AT                V                                .                   |                 n   ɧ              
   
   !T                V ͧ                    T                                 x              v   '                    <T                   ʧ              \                 pS             o              xڧ              zΧ              h                               r  
            h   ;o    ç                                  V                  #              `6              xDT                                       T                                  jn                       R                           &                                  V               @                    /                 *              ,                 8                   @#                               '              $                 R                    R                :                    
               ;o                  .                                        R                                 (              Z                                    D   =                 S                   S                                        R                   Y              r                >              L                 RR                                                         R                V "              ^J              $                 V_              ,                 @                T                 0                                  ZJ                 ,              V  R                              t   6   %              $                                                   .   R             	   	                    yR                V                                R                                                    d                    N                 1              *                 M                x                 t                      2              ,(                       R                                                  NX                                  
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                       {              ~   QT                   z                                  1T                                    S              ^   .                    n                                                                    vv"T                                       N                    O              vv                                     f                 b                               "  ^                               ~   n                                    j   p              z                                     R                 T                V               eT                V +                 j                                     t              T                                    RT                	                        e              vY                 `8T                    o              |                 nk                                                b
                              4  Vh              r                 >   -T                V               |              |}              p|                 z                                  R   R                                               /T                c              ~                 ,T                V               |                 |                                     x                                     ]              s                               z9T                V                     (U                                     b                 X                 xqb              rv   I                 `b              IJ                 j                 a              j   ժ                 tbJ                 I                 XmJ                 a                 b                 v!J              hb                 b              r                O~                 I              
   lI                            T2  J              TJ              h      a`              v   }              d   *   -                 `ۈ                 I                 I                  J              |   J                 I                                  ~1J                    	J                 I                 VI              `                 l   I                                 J                0b              ~la              ~J                 I              ~r                 |b                                     I                 I                  T                    I              Z   /b                                      I              "   NJ                                  (  ~I                 w              b              Bb                 xI                 J                 a                 `a                 rJ                 
                    a                 J                    J                 ZI              xI                            d`              ~   I                    P              p                      r                 @
T                                 "   A  
            &           [                                                    Rl              P                                     P_              l  D                 Ti                 I              NTv              h                                                         j                                     T                 Lw                 g              lD                      {                 X              h   b                                  \m              NT\                 !                 ]                     ^              f                   `              T   G                 Rn                                                   V              F   S              d\                               p                                                         Z                                  R                    y                 R                                     P              X%              v                 o              Pl                                        &              Y                  \  X         P    W <V W   V   @    W U pX V      V V W  8V DV 8  <   W U \      X  DW W B ķ     d    L D   l P W W V     $  ܋   ط 0  ,V \ xW  , V      W [ X W D  y               :                 p                 N                                    *                   b                 F              $   0f                                  V              Hv                 NX                 WT                V                  ^                                  l                          :                 #T                                 B                   N              "   <n                 G                               L   p              &                   h                 \              P                 *   )T                                 P
   a              rBZ                                     T                g                            J  pD                                                N                       T                V w                 NH                 \                     T                   `                 P9                               t$T                              
   D3                    M                 h\              [              `   T                V z              f   4                                     h                                  5              p^              R   B                 T                                       T                V               x\                 +T                   2                 
   x                 f                 ZT                              Jc                  T                                 n              `                    ^F              F  ~                    e              (T                              >X  T                   i              vZ              l2                              =                                         .T                O              x                 
                    e              "                      %                               y                                  .                                  .     yV              &                                               
                               B                                 (                      3              ,     x                                   C              "                 .                 
ɵ                              A                              ^#                 F                                  9                   "  D              
              2                ,                Й              ,                8  G                
   ,              &                                 
  Y                 A                               @     U              4     j                                                -              d   8e                Z                               D                         I              /              D  :                                            8                                    ,                77                V                             ϐ                            d              L                @                                               *  V              v                    i              4   ie                                  _ X         P      | d 4      ̩  Ш  | 8  \     0   \ Ԩ H    \ Щ  p  x l  ܩ  (  @        `       X t     ԩ <         P    4    l L     p ,  ب 0 	R                   z9             ,                 @   D              :              <	              ?  t                 T              TN                               l   C                 G                  6              h\l                 2                                     z                 >              T  r              hE                R                 \X              <                    <                 Ve              @                                       ~T                V _              $                 4              `>              >Y                 
                                                      j~                                  ^1              d  T                 QJ              b\+                 @S                    y              B   U              "                       0T                                    6                                V   h              @u                  $   Z              d   F              Pp                \                    M              n  \9                 D              N   /              `                                     #                                   `:              xF  q                                  l   0                       L                 n              ^A              b"              n                 W                 ;              nP@                    H                     5              fi                 0p              @   _ X         P   i  ,     4    ` 4 <          D    <      d L       <  t       0 8  \ H D 8   P p  X \ |  `  $   h l   h 4     T d      ( x <  ,w              V             4               T                             t   *   S                             @             Rn             N   T                V                                    N             \                4T                                 V   z             V                              j   T                                64T                             S                             d
                      	T                                                                 V             `  D             `   T                                                                   F   	             b>                                                                        p             `                ZdT                V                 T                V                 T                                                                
                      |   '                                2FT             V                                                 hf  >T                V              Z2T                                VlS                             
                      H                                   B                N               b                                                                                
   #                             H  )             d                   T                                JdT                V                  T                V              f                V             b!             L&   S                                
                         S                V              V                    1             ~T                                d  F             PUT                             B             $                                        6a  
                     h              
  s6 
               ;o    D                 (	              X
              x_              0                                                                        2#              8                 D                 \              V              |  HE                                                     ")                                  2                 T                   4   "                    B              8                 T                    KR                                       g                T*              v   2   3              v                    
                                     T?              
                                                      (                 ,              ZP$                 6              "                 HD              J                                  .              ZP                 2              P                 @  Us                                                                       R	                 .              &   2                    T              t                                  H                 l                Z              0                 "   0                    9                 2                 L                               4%                                                                       f>              n\                7                                                       &e                  
  \                s                                 z X         P   <0	<  P   T  t D     x 8 H         0   D   D       0  X  P        P ,  H  H    8 d  L    <        ` l h ,  4  p       x       OV  X         P   H (N X   hh <C  #  h  TM <k g <       g  g M      P   < 8 f  / $     \ E     f f g   " A ̴ L ; @g h  ,h = $E g  f Xh g \f p $  Xg   h  M       Y  XL |h   l9             8                       )                 N                                 F9              X              n                2                    "S                V               R              2S                V &                    R                                                %R                V (              D                 XP-              2S                                  *              t   S                V                  .                 $S                                                                       "   T                V               :                   R                V                                   2   R                                                  H                 1                VcR                	   	                    R                V                                    0f                                                                       P                    H              VS                V                  N              6                       gs                                    X     T                              F   T                V }                 ~                 R                    z                                 t   2                 X   R                V                  .                 4                 S                V                  $B                8R                                 XR                                     V                 T                                                      T                              n   R                              0                               lb  %              VP              &                 H               J   S                                  b<              .                                  DB              v              
                                          J              FH'                                P                 P8                                     L              F!  X         P   h@   (        x  (            P  l   h       t  x       0      \    p  d    l  0 `  | 8      h   D  <   , $     \ l L  X D0 k  X         P    PH $ z O py / I z g y O O P j J N     y  ȫ ̂ N Hy  |P 1 z y y  I  0 O p { { z PO  Lz @z     T dz / {  lO y z ; y 0z ly 8z xy pz Dz P pP (P d^ { `z Xj P 4P / \y `^ <P z y O     ` O Ty / x \               08                                                        T              R                V @              L              l                 U              H                    HR                                 ZR                 r                   D                 JR                   %                 M              DLS                V               G
                     P                               x   xR                                 H              z  >              R                 X2gR                V               z  <                 R                V                                    T&              x  D              J                                      B~  A                                     H                 zR                V               bX                T                    R                   p                 F               V              R                              J                 N   `                 6   _              L                 L9              b                 `   M              B   t              N                                                          NB                                  N                 
   [                                     V                                  
                                        uR             4                                     `                    R                V                  @$                 3                    (              lL                     nT             V                  lR                                    BX                 Df              \  .R                 b                                    V 6[                @h                    6             <   K6                6             @   "6             (   r6                E6                @6               (@6             (6                 6                 6               "6                6             (X6                    '6                6                .   W6               j6                -6             ]6                6             D:6             $   .6                   86                
  (6             bC6               F6                p6               x6                    &6                \6               [6                a6                k6             "L6             06               6                )6               d6                  6             h  Q6             (   %6             T06                6             f6                   6                x7                V S6                6                v6             0   16               O6             4   c6             d   /6                   !6               4n6                >6                6                4D6                6               36               6             u6             :  +6                  6               6               6                "   m6                .                 J6             " 6                h6                L   6             (   ,6             " 6                ^6             FY                 2l              >  Iv                                  a              J  KV                 p                 (l              ,                    K              ,   l                 F)K              (     Y              4a                    O                 ʏ              4ύ                 U                    %l                 Z              l  w              tS              $.                 (   V              _              FO              2<x              
"   p              .   dm                  l                 b              2DZ              "   P              ^   AV                3n              4h              &      j                   zm                    =l              :K              *k                 Wl                 @   ?d                                  @  y              2   a                                  p                 G                 ۔              :J[                 4&l                   [                    k                 [u              TZ              
      w[              6      O7                   {W              ~   O              <K                     6V              2   ,l              4   mR              8	[                                     9[              <K              "   /l                    ȉ              &      k                 s                 l              xX                  z                    1h              4   ;              T                VW                 Dg  
            6  ;o    (                 q              >                              0   K                p-                )              L                2   2  W              T                                                  F              X                 H                j                ;                   h                                      T  R                b                 @              N     <                            \  	              L                   I3                 	   V                  S                              Z              H  (                   8  B              N                            H  0              L                
   &                                  |i              
   n              X                   p   ?                 \              ^L  Gg                               |                 *                g              (                 J     ׂ                              \                   j{                                           Rj                z                                  o              J  g                b/                               V                   2   [g                 7              .  p                            J     ;              t   v                 L                   3              _              P  D              N  C              d  P                }                              X                   z              8  (              
                    ,  5                 Ƀ              9              J  N                 J  =              
                    /                 S                               0   '                                  :  "                                  ~g                 H  A                                0  |                               
                                        5                                     T                 B~              2                 <                 H              0                   U                               l     N              T2c              &   ,                 R                               B   !                 F6                 k                                  Lm                    .              j   8                                *   b                 3              Ly                 \              R   "                b/              n-                 6m              T<]                    )                                <x  tR                V H                    I                               ,   ?                               t,%                 K              >n              @   4              
   P                               [                 z2                 t                 F                 @                                     6M              *                 *   &                 ,              n              0   '                    `                                  _                    l                 (w                                     *              z                    J9                 $#                               :                 `-              h                T  Z             Z                 *              ˙              4   `                @`                  *`             D     Y`               B                   {B                   7B                J   oB             <      B             h  A             "
  #B                 B             MB             
$   EB               VB                I7                V B                ~B                B                  B             ^  B                zB             NFB              tB             "   F7                V B             2      CB             &*B                
Q7                V +B                   AB                7             N  g              JXR                V g                Kg              g              D   =j              ^R                    g              @   g                    ŉ  
            *   ;o    sg                 R                 g                    Aj                 
   g              J&g              BTR                V Gj              N  g              B@g              (      rR                   (g              tx  g              D8g                 NR                    gg                 F   ;R                V g                g                  lg              :mg              >ZR                V g                 *SR                    g              D"   g              @   g                    8j              "   g                 QR                   g              2      `g                Jg              F[R                V f                 pR                V g              2   S                V g                  T                 g              8j                 fLg                 }g              (NjR                g                 $/j              ug              `PR                V f                    aR                g                    g                 g              *<g              ,>`R                    _g                 |g              <g              ("   Vj                 g                    kg                 g                 xg                 g                 cg                 Xg              "   g                    hR                V g              :   Fj              Z   g                 g                 g                    g                 g                    g                 (_R                eg              6g              (      RR                   Dg              0:g                 OR                V g              4X                       m                 m                 8                 m              Rm              D   u                hm                 >m                 (n              |~   m                 ޕ              X   m              R               <n              0   b              D              Xm                  m                 $                                                      `              *   b              "                    jR                     2R                V fR              @                  b                                                V                &   V              (   {              
'|                   NR                                   ?R                   &                  IR                                    i              ,     kk                 Ȋ                R                   k              %                  {R                y                    Z                               D   !a                 Zu                                   r   }Y              -|                "Y                <R             	   Ή                 \R                 )Y                 ǉ              $   JV                ̔                                     DR                jt              
  HR                               T(              y                    `              nR                   {                            *qR               6              "mR                   Yu                 :                   k              &   o                     JR                                   M                               2   iu              "  щ                 Z                 Ӊ                VR                                                    "  ˉ                 Z                |              "  vu              "      Ki                :Z              vY                    Y              iR                 AR                              >                 $  FR             
   K                7                }7                                b_7             &  f  7             ,                   7                     7                7             4   8             "  7             J  7             7             D  7               7             |  7                7             "   7             0                   B7             4   Z                    u                 
R                I              .O              4   I                 u                 R7                3h              
M              *   /M              (  9R                   V              ]a              $  i              7R                V qs                L                'h              {M                    i                    YR              "gM                /h                R                   @M                    Q              qR                    Ph              $   O              ~   :7                Oh              dX                 /f                 V                    O                =R                   7h                                  I                    Ch              nYR                i                    .f                   HR             V V                 V                b7                .h              ,  7                V #f              V                                       cX              L              X              
I                J                 f              I                 <h                   =c                \7                V I               3R                V Q              "   I                 N              (     &h                    ,R                b                bc                 YW              FZ                    Q                V :h                0R                   L              
   GR                   K                 
  1R                j\                 ,h                 M              ;c                    'R                   'f              
     ~R                M              ^                 R%R                gQ                 F   @c                 .O              
     R             1             
]7                V 1               1               2                1             &   1               1             6  bR                   1               @7                V 1             0  1               m7                   1                                   1                P7                   9                 65                7                V `                &   1             &    2                                J   ?7                V 1                41                (   Z7                 1             (   1             1               1             H5             *1                ؗ                 1             81                4R                   1                   1             4                      1             *1                 5                    D                1               :o7                   <                    1             0   1             1             (  1             >7                   1               1             *   h7                1                                    1              1             1                5                5             vj  1             8   1             
      1             N1             >   1                6  5                  1             ^  1             &1             
   V7                1                1             6  1               1               1                1                5R                V 1                 S7                V 1                %              ^   7                   1             U7                    1                   1                6                   1             4  Z X         P   ? j \j k ( ` j ; g `k j  k j j j j       p <  Hj Tj j i |; hj h D3 j j <   < 8<  j  h xS     xj j  8 j  i tj s   {  |j ,g j i i n j h j j g j l j   Ph j j =      j < h <j C X X         P   ȃ&	h   Ȓ ̒ <   0 ԓ ؓ L   H ؒ     P 4  ܓ   ܒ     T < P     @  T     ,       t Ԓ   0  Ē  ` $  |    ē    ȓ ̓    $   8 4       |   Г      3              &  $`                	`             Q 
            h           :                   4                :                  _9                   :               4             0  $:             ^  4             *
:                4             :                9                Z9                :             *:                 4             0   :                $   4               4             L:                 4                :             2j7                   9             84                
g9                Re9                y9                :             Vq9                  4               &:                :             *k9                s9               v9                F   :                x9                9                c9               8:                )9             ^m9             p|9                   :                :                9             2   :                  :             
   :                4                <4                   :                 :             04                9                :             2   4               ^9             l~9               .i9                    }9             h   [9             (   :             
  *4               4             84                :                9                {9               :                9             "   :             B   9               :             B                57                   uB             B                eB                %7                   aB                 .7                   \B             (B             $
B             
     B                   JB             
B             B               G7                V nB             $`B             (   T7                V 6B             "     B7                V B                lB                    jB              IB             
0,B             .   TB               pB             RQ 
               ;o    GB               f7                V B                   s7                   "B                   QB                   B                  B               C7                   B             2  )B                B                  6             V ]B             DB             sB                 e7                ^B                6                'B                ER                LB             $     B             l   bB             ,j                   hB             &  1B                   YB             jiB             $   B             fB             
  R                =B                *D7                9B                [B               B                0B             5B             j   H7                    PB               q             D     p                &  p             ol             N   El             H  .   l             \  LR X         P         P  t `     p H P (         \       D p  ` ,   H L   |                   (  $ p         T   , D     h <        T @ H~(	P             8 Q             B  7                V QQ             ~fQ               Q             V  Q                  7                   WQ             ,     !Q             6  nQ                  +7                eQ             jZ              37                   uQ                
  wQ             	Q             +Q                   7                   lQ               -Q             4      HQ                   4Q             P  EQ             2  17                _Q             *,Q             >Q                SQ               `Q               J7                   ~Q                IQ                fQ               Q             YQ             (  <7                hQ             P  VQ                   kQ             ,   "   Q             ZQ             
   yQ                   qQ             Q                7                V iQ             0    Q                jQ                &Q             $     X7                   P             PQ               '7                ;Q             `r   P             
  XQ             :  7                V Q             :   Q                   |Q                [Q             4  mQ               "Q             
FQ                 8Q             >  0Q              }Q             \Q             P             *      Q                   Q             6Q                   #Q             7                   Q             R  *7                V Q                  cQ             0   Q                L   (Q             7Q             (   c7                BQ             :  Q                27                .Q                2Q             ,  dQ             CQ             D   ئ                 d             V     d                7                 d             
   R               tR             H  vR                R             +S             T  \R              S             <  R                                <   R               R             F   t  S                N  R             2       R                 T  R             d0R                 @  S             "                      <R               ZR             4                      .R             X  Z"S             R                              
S                R             \  R             R               S                S                                  5S             Z  	S                @  Z                Ȟ              (  Z               L              B   Z               Z             J   ߎ                    Z             
      Z                  N7                                 
      Z             x  Z             ,  &   Z                                 7                                 Z             D  Z             &                 ,                   6                B  BZ               ϭ              6  Z             b  Z             Z             &  4   Z                              6  Z                                 Z             Z   :              Z             J  Z             =  (                 j                V                #7                   .              h  "              f  6                V Z               M7                   {Z               ʭ              0   7                               C              $  W7                   Z             j  Z                N              @   Z                Z             X              <  Z             :                 "   D              ,.              l              6                  Z             8                %                 07                   e                rZ             @  Z             R   7                                 X                2   Z                N   |Z                Z                ޔ              (   Z                              2Y7                    Z             u[             6                k[             e[             
[7                \[               c[             
Z                -[                ![             Z             >  6                   [                ^[               R[                  7                V O[             Z             .  [             &     [             B      97                [             .   P[             B     &7                   H[             7     [             ([               >[             +[             "  [             6  W[              ,  U[                r[             *   0[                [                    '[             8      [                Z             0  [             :  87                V G[                #[             3[                [[               7                   Z             ,     =[             f   @[                i[             F  V[                ^   E7                   K[                 7                    &[             &     Y[                ;[                =7                   Z               L[                S[             >  ;7                   Z             6                    g[             ^s[                X[             [             ,   ,7                   j[                5[             [             8      Z             0   Z                
7                   .[                  h[               [             
7                V [                   )[             P  q[             Z                    [             &   I[             7                V t[               [                7                   C[             p                 R  ȹ                            tS              l\                <                   t              QY              J  <   ^                Z              @   r              l                `  ?              (  ̹              P   ^              v  .P                                              (  %              $   7             \  ~7                                 7                 7             <                         7             l  7             h  7             <  :                        7             ^  7             &   7             7             >  7                   r7                 7             v                      `7             8   "7                   7             @  0   7                n   7             7             b  7             t7 
            ^                  @   ފ                 B#                d                  V             >                                  ϊ               4                   Ԋ             
   T               N                                                	               L,             R͊                            4                                             	   ݊             B"               Hv               P                                  ֊             ~                   h                               V   @             $                                   j>                  Ɋ             B   7                          8                                                                               V                  )                                Ê             L                 ڊ             t  6<             T     Њ                                                               ~ߊ               ,8                          PD   Ċ               >                  0             ؊             P     3             ,               Պ                &                                .                               r                                             |  ۊ             p   =                                                            Ҋ                !                >                                  Ǌ             H   ׊             |  x  5                             :                i                             ^  /                          ъ                Ί                -             8      *                             b(                6             @                                Z                                               ˊ                p                                 D             6   b             2               F             ^             \               n               &R             8   K             <  <               ~             1                          6   XC             &             t"             B                                  z                   0             x   +             j  Ԃ             L  /             d  >   B                            l                  ͂             @   D݂             H               L  H                  b   A               $                       >             (   fނ               ?             6   (                            \  Q                                R  T               |7             *tۂ             V   ς             {                              ^  R             ق             xZ  =             -             h  ,   $                            ~N                                l             h               8             l                 T8               |7             >   7                                 R7             J  7             *                   7                d                   7             7             (                   u7             v     "f592 (this will take a while!!)";           f592 (this will take a while!!)     7 
   qEigenform(D592[2],2600); 	" X         P   ;	2 2 3 3 4 4 3 H4 44 4 p3 4 83  3 4     ,4 2 3 3 4 2 4 03 @3 2 2 04 l3 3 2 t4 2  3 2 L3 4 3 @4 4     l4 3 \4 L4 4 <3 4 4 43 h3 3 4 4 3 t3 2 d3 4 \3 `3 3 P4 h4 3 2 2 3 3 2 4 2 2     84 3 3 3 d4 !             |
                  [             `4   %               bL                w                y             ,             V"             :                <   p'    "DONE!!!"; 	 
            2      ;o                 ^   r  \             @  j             F   C             .   =             R                               >  W                             \                                d  (                                 Lyx                                          :             TQ             B                      z  h                r  c                                              (   |  B                   G                          Z   N                J                              V  H                <               b                          f             R   x  >                             $                                D<   1             l  bn               *  g             `i                             4~             .     E             PT  '               J                   ^             N     d             *   h    
               ;o    k    save "valentine.s";              6             ~r             f  LD                            Z  N               T  H                             $   {             F             \A                ~   s                I                                /             
                F  ;             ~o             ~  w             v               e                            @  |                #             V  jl             *               v   9             jd             t                               2   L <
           1
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                  4     |     ,                                                                                                        $      4                         4               H                  H                              5          4     hG          6     3               ,5     5                   6             5     4     <6     $4          I     6     5     4     P4                  F     5          I                4                       4     lH     4          4          5     5     5                     G     P      i      i     8     h          ̡     P     G                     J     <     0     f     5     H5               D             @     `     G     Ti     0          pF          4I                  F     D     6                         `     p                  l                              x                                      Т                                                    <               l     Ԣ          D                         h                         h      ,                (                                           d     @     @                    |          L     (                       $     0     h             D                                            4                                   (      p     h           ,      H     ԥ             Ȧ           Ԥ          p     P            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                  _U               R   wU             <  rU             0  U             ׄ             J                                L  0 X         P   X	[ Z Y pZ T[ ,Y Z [ X dZ  \  l Y Z     ` X Z Z t[ Z D] PZ @[ Z  [ @Y xZ [ ([ X[ ē  X  TZ  p[ |Z     t Y ]  Z [ Z Z Z ̓  [ Z TY   `Z Z ] X  [ Z [ | 4[  Y Z Z 0e lZ Y tY     Z [ [ D[ Z X	X~ X         P   	      H  < l \ Љ  8 $ T     L  ĉ    8    @ $  p  ȉ ԉ   Ċ  Ȋ |   Њ      4  |   t    ,  "          ܉ ܈  d  0   L (      ܊  t      %             R   e 
            2                       	                ql                D  9              >                n   /              V     l              f                C                                                  p              H   T  uJ                    Ƹ              Z                 2                      &              t  (              ~  
!                                 6(                                                      ;              N                 x                   4                 Xȸ                (              ^{              :@   A                                    -              (                 U)                              d                                O              n              v  C                                   f  ;                   *              2v              P                     $$              p                 Ǹ                                            j  ָ              :h               j                <                  5              :  M                   ig             4             8}             zF                  Pf                z  J                                                      T 
            R          l                                                                       
   D             zr  R             0  h              *   F  I               0  1             v                 p                          0     /                   i)                   $             r  6                  B                                           "   xm(                                $   C                               4             *  ^C                                   (  8                p               Z                               V   L  i                                  J                          `                  3                I                @               ,             rD                                      N                                               ~  ?             
                    x  y                             >   pSl 
            B   ;o    0             p               9             B             `             Z                @               .               !                             @n                                <                            
                |               t                              |             T  &               VC                               )                v             |               <                                             F             f  B X         P      $ 0 | L    @   8  L \   x     l  |    4 H    d P , T ` (  @ 4                 8   T    (  X   h l    p    D        $ (       B                                I              N                                     h                  F             |                FG             4     1             <                T                  2                  (             B$   l                (             0   $                 &                   .     `J             ,   &             V              ,O             T                F     '             ,                &                                  3             H   (   9                             I                   J             (   "   g                                              C             :                0   5             $>              4  >             B                 *                  8                           >              B               .                  |)                   =                                "                                             *                  C                 :             0             .             pH   ;4             
   Z   )                   4             l(  =4             4             \    f4             84                H                54             2  \x                4             \   j                   4             zi4                4               q4               ~  24             HN 
            $   j  ;o    V4                  V                                                              1               L 
              Q             d                             l               h   ! X         P   `	\   41 L  @1 X L2   $ 0 0f        \    1 (     0  `1 1  1  0 8  P 1 L|       1  .  1  1     x <,  H `   P   L1  1 D x1 1 X0  (1 P   1       0 d    ˸ X         P   P	  L d  h `         0      8     x     8|  0 |  D  t   `        $ T    p  X P  d t   l T  |     H     P  @ ` X     `   P ,    *              n                  N  r              bR  !                \                                :   ]                 #                                                   I             J   p@r              Z  Dir              X                N                p                      2                  x                               )              |  i                    Br              0  \   (                   l              FH              /r                (                "                 r              |              ~                   $   r              Y  nr                Xr                                 r              f                                X  Ӛ              L   r2r                                             %                              R   ^                              T                                                  D  
r              $                                *                                   P  r              J                v   pr                                v   br                                          h   L@                <x                              H  Tj                              0  Zr              z                z0P                              4  I                                              r              :   V              r              n               P   j                r              :  D   *r              tN                f                eT              V   ^                r              
|                             Z 
                       D3 X         P          t p      4  |  4        X   d           @   $            ` x    @ l      H  D   P 8 T   , <            h \  \ s      X         P   a	        P    P   @ ,      l    ,      t  | d  0 |  x H   p $ L       L     h     ` p H   0    X  (   \  D   T       $   p	 X         P      `G E E G PF F tF LG G DE E H I pF hH F     F XH G PG F PH F F F F G E 4G F G F F dF H hF G @G LH  G     H G F G lG TF tG ,G F F pE F H $G G ,F  G <G G G F XG F G G 8G F H `F G HG TH     F  H G xG F     V5             2                    ×                              g             
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 X         P   dµ	' & ' 8( ' ,( ( T' ) ' ( ' ( D( `( )      ( ' ' (( ' H' <( & ( P( ' P' \( 8' ( ( H( ' ' ' ( $( D' 4(      ) |C 0( ' l' ' ' ( ' 0' ' T( X( ( ) (' X' ' ( ' ' 4' ( ( ' @' & ( L' ' x' )     ' ' |' ( ,'     W X         P       ! x  ! " 0! !   d! ! ! ! @  4"   ! ,        X  ! |! d  <" ! $"    ! 8  ! D    ! ! ! x! \! ! P  p! H      ,! `  !     T! 4! D! $!    ! !       ! T  ! ! 0" ! <! !   h  \  ! ! `! ! ! (      H! ! "   !    ֓ 
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   P                   #             r#             B#               #                                 `#             X   }#               6   #                BI                !   #                  q#             ^  @#               ?5 
              ;o    Y#                T#             lb   #               nh#             :                #                @/ 
              V;o    #                #                 u(                #               p-j                f#             F    ^#                   y#             <  H                    #             \#             :Z#               |                #             ^  5#             D  A                [#               O#             f   2#               :#             V  "J                7#             N4j                x#             0  Q#             2   #                 ^0#             #             v   p                    |#             \  *R#             \  H#               _#             z                    #                #             #                pI                =#               d#                b#               V#             6(  #             $K X         P   W	43 P4 e 3 2  2 2 3 1 h2 2 1 2 3 L5      $3 Xe `3 1 , l2 hd 2 0 03 2 3 T3 1 ,2 e 1 2 2 .  2 3 3 T1     he 2 \1 t3 2 1 2 1 1 1 5 1 83 	 2 De p2 p1 1 |2 x2 0 e l4 1 |e 3 3 T2 1 02 2     3 2  0 <3  ˸y 
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     i                	               
-             D7             ^  PH             &r               BW             (                    E             B     L                               ф             r6             D   uI                   S             B  +                  OJ                   9             B  O             X             `             Jӄ             l                N.                                                l                             *               htI             `  \             &   H                   c             "   S               7             &  ]               $[q                
   e             h               OD                   !                "             :     ?                                 (                               _             P   ߀             J<  J             @             *                "U             \                  I                   R                                                                   4             Z             
bf             P1             x*             t  J                  F             p     ;             <                     B             =     ,I                .             ~                                z      I                    i               =             t             d  UI                   g                {                   L             p'             \               j"   M             `                X     Sx                   (             T               N             d   a             Z  t               $             V&             n   #             d+             v  0                >             ,     :               &   E             T  V  )             L                               F\   
                       ' X         P   h	hI pH I I H HI 8J I <J I lI `H hH H H H     H HH I |I H H XJ 0J J J TI H I $J PH tI H I XH I I I LJ DH     I H H H dH $I I H 4I |H (J J (I H TJ @H xI H @J H  I H hJ I DJ 4J I H ,J ,I I I     I pI J I <I      o                pn             dF  n               Bi                o               n             H   6   n             (  H                    n               BH                n             Xn             V     n             n  fn               n               o             H   n             n  W)                n             n             n             6   :   n               n             X    n             T  n             rn             Vo             8:  XI                n             Hn             :  n             (    n             b   n             <                 n             <  0  n             xn             J  n             :     n               n)                n                  n               n             lI                n             \  n             8     n             h   F   n             *     n             D     n             &  o             
I                n             nn             ,  n                  n             Ln             F2   (                   o              p   n             Pn             ~ n                   n             n               fn                $  n             Z(n             *     n                )                n                  n                J                   n                n             h  n               n                fI                    n               n             0n             n  n             
n             R 
            D;o    n             n  ۙ                 J  6 X         P   4  , T+ , (+ p* * * * + * * + * , p, +     * +  + P+ + + T, + l+ * D, * + + P, * + 8, + * ,, * * d+     , + |, * + ,  + * 4, + + |+  , l, , * * h, * + ,+ x, + `, * + , + H, 4+ *     + + * * + h l               t   cl                8f             p   l             T                     nl             t  l             Ml             8   6-l               el               `D                l             Rol             d@  X                l             P:^l             l               l               yl                 l               Dl             t l                  tl                   l               4                zl             $  l             H4  kl               UD                2l             f  "l             |  _l             D  Rl             >  l             h6l                 [l               "   l               gl             n   .l             b  l             dl             F   ?l             T   Xl               )                l                 l             :l               ul             X:  Cl               l               Gl             ]                   pl             L%l                Bl               @I                Fl                *l             B   &   Al             4   l                Kl             V    'l             l                h}l                al               vxl                /l                j                ;l             *               	   5l               j   {l               (l                @   l               l               6   Vl             z   Ll             P   "l               t                l             T  l               	l             $  R)l                             T   6             S               a             }                 X                            j               (                ,   I             z               .   eD                
   8             8   %x                             .  z                             b             T  A             f  C                             V               "Pb             B  c                               ,  G                0             nB                                X                x               h   \]             P   Jq             0  E             ,   ;             h  x                =             8  ,   .             J  u             4  f             >   N             ~   I                             |   ~- X         P       t  < d  @ P L       4  (        d D D     8   `  X    | < x       $       \   ,     h   @ h 8 < x    p      T       0  `                  D  0             7                8  8             >L  
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                $j                            .                T               8  R               b   g             p  |               "   N                            2               R               T     K             D                   ^                  J                                 td             |m             J             ^                  I                             4                              x  
n             :             x  k                                         
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               F                             t   7             >                                 .                  A                             d.                             H   I                                <                                2                                 "             B               2   $   )             #                   $             Z  2   i                             T                               
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 <  . X         P       l     h ̶  X  x  | ܴ \     x        4 $       , \ p ش ȶ   Զ  H     ܶ d  0 |  4  l , ( d    ĵ   t  t     `  @     ̵ <     X  8 H     P                              $                %             %                  %             dZ   y%             r  H                   %                 m%             b     %               8%             8     %             %             &   A                %             %             @   %             R  ~%               v%                %             "                %                ,  %                  %             ^  e%             Z%               h%             t %             l   %               pY%             n  %               o)                
   %             %             F   %               )             r%             v  %             H  T%                                          `     H                b             .               t                                              6  :                            @  \             ^   5                                                                 9                
!             8                  [             f                   B                 ZD                               !j                                  :                   (                  '             
                &3                          .  +               0                 6                                     )               VT               2             >     	             R     X             .                0             Z.               ,F               O                
            6   ;o    4             8                $                  &             
               8                            (                                                                ,                  7                f                  W             N                                                   $                f               G                #               Z;I             3                                     I                             T                  A                >                J             L                                  $              $                       ,             <q X         P         X ,         \  $ ,    x               0    \ 8 T   (   < <            p      X   t      P   8  0 ( `     e 8        h          L      t    , H                   V               v,             *   I             BJ             |^   
               -               u             V                                 >               N  E             (                   &                H                ?             "     H             @C                                P             v  w                   [               b  A                b             6  ۻ             `                  V  `             ~   a             t  ^H                 +               G             \  "4             @                P                  l-I                e             *D   \             f  Q                                JK)                                            |             2   d|             *             n   (                            :             &  ~                   !                l  L                  Q                  i                               VI                <               >             x5               "             v  8                D             0   r  ;             :   6             (             	   	                h  <޻             r               '             c             J   0                              h   ݻ                                             d             Z  x                T                                                               z             H             !                >                $     V             &   M             n                 .              \  d                                 mI                g             R             Lh               L6   P  X         P    9 ,: < |: 4: D< 7 < : : ; : 9 8 T: 9      |; 7 `; > < 7 H: : < 9 : = : 9 D: 7 : 
 4; 9  = ; \8     : X> <  p; P; 8 8 8 9 : d: \: 8 t< ; `= 4< ; : 9 8 T< ,V <  h; 0= p8 8: = =     8 @: ; = ,  f                ].             ,   (  -             2                             v   I                                 <                                                 ^J                ^               N                w             
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            `;o    b 
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            8                       ~  N                 e~             H  -S                 p4 
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 \
 X  @/ , Ț H h8       L |8  8   9 4 7  7 D 9 |6 7 7  9 X8   
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 7 
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      L
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 
     _             v(   X         P      d7    ,  0   آ \    |F P     G  s   H1 8 t   7 G   p `7  Џ  H $  &      L  Dr  H $Q h `  C  ( L p $ y g    P N (     ԃ   i - \  ?     <!  X   #	             ,؝               `                           ,     xD                                                  j   p    
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  | X    $      H  L      d t          ` D  s X         P   $ \  t  p `  D   X | , = P       @   X  `  < P D H X    L L P              \   @         L 0 d x  4  t   D  < (         0 d ,    (& ʝ             z               n   X         P   Hc&	G H G 4H XI DI H H H G H H HI H H G     G H G I HH H PI ,I G G tH H |H 0H H H  H LG G H tG dH H H     H ; pG `I H G \I dG I G G G G G |G (I H G LH 8I hI H lH \G <I xG G $I I H H lI     G G G G G <  r                              T             vV                  0               >             Fl)                               X                               xW               
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     p 	 	 < 0 Q$	 X         P   U$	$ l    L    @ <    p   \       t  | h 8      |          l      | h       P  y `   p  8       X  T P \ (   l 0         P `      ,              8   q                 L                
   r                  j                            G X         P         x l  h 0  ؊ @ ܊   | T      ` P d Ԋ Ћ    p  H  Ċ   h 8   X L 4 ċ ty      |  L   D \  t 4    | P  ( $          $   8       ԋ l ̊   h$	 X         P   p$	   X l t L ( ` `   L    $      4          H     P 4             @      , @   8             T  8    D       ,   $    r  X         P   r$	<n   L   @o n l 46 n     o   n n (!       <o n   ! Xn Tm n o $e H m  6 n m ! n   6 d  n   n       0n to n do !   m  ! Tf D6   f ho $     po 5 p  |   Hn Xo   $! To <!   0!           n  l n     X         P       D    x  ̦ \ D d  Ц  l (      D   ȥ   8  <  @    \   H H   @          X Ȧ  ܦ 4  ` T  | \ ԥ   $ H  (  h   t d   L  <       \ p `  p$	=                                       |  c                F                                 t  0             \             >   T                   .                '             H               j  ^             8  (             dn  6                                  [                                N             D   ^                            B                                                                                  T               Z                |H             @   h               R               ,D                                  ސ             x                	   2             nX                             n             ,   PH                                             )             9   M             @W               P             `  I             8&               F   f(                                  I                   &                l  3               <               O                X         P   t_ ,         l `    H      ( h 8 (      L    x @     X x 0        ,    $   \ X     <    t p   | 4  @ l      P   ,     T    \ `` c( X         P   9 0H I G pJ dH F ,I J H  J G H  G lI XI     F H lG 4G (e H  I H TF E F HG tE $H G G H  F G F K H 8J     G ,G 5 H tI 8i F ,D <K H <H H <G `K J I xF  I hH $G C G J i 4K H \G J F `G H lh     F J G I f @>                  ٔ              |  n                rh                               d  x  . X         P   <P	X l t       8 p dx h        @   D  x x     v     X T   x    ,     x   4 H  d   D `   X z           , |  ,y          4 <        eY X         P   Hc&	` _ T_ d` _ ^ H_ ^ ,_ _ T` ] _ ^ L` _     _ |^ ^ t_ D_ ` _ _ \_ ^ \^ _ ^ ^ <`  _ D` ] 4_ P_ d^ _ _ ,`     _ @_ ^ ^ h^ _ _ _ p_ ^ (` _ P` 0_ _ l` ^ l^ _ t` ^ _ ] $` ` p^ h_ ^  ` _ _ _     ` _ _ 8_ ^ <  " X         P       <s s s r \r q s s r Ls r `r dr hs r s     r ds ps s ,r s q r r s Xr s @s s Lr r 0s 8r r r r xs 0r  t     s s q q r s r r  r r s r q s r r r s r q s s s r xr s Xs r s r (r |r     s ls r s r     2 X         P   @$	 | l   ` 4 ,        $          \         0  L t     P         T  <      (   H $   0  x  d   t h    `          X t      X         P      T $ | 4 X T    <                 p  ,    @    l  $ \          D  L    ( X @ x L  |   8 d    `  \        H          t      X         P   $	2 2 1 1 x1 1 1 h2 02 2 D1 0 0 1 0 1     P1 t1 2 2 1 0  1 `2 1 |1 L1 2 1 `3 0 L2 2 T0 2 2 @2 <2 T2 X2     1 l1 0 0 1 `1 l2 2 1 2 1 1 2 1 1 0 ,1 \1 1 1 1 1 2 0 <1 81 42 1 $1 2 d2 0     1 2 2 p1 1                                                    l                    2                "   7             X               !                @"               !             R  <"               !             <  !             Z  !               !             `	"             R  F!             N  !                4  !             h  H!             A                !                 !             T     "                                !             |  t!               !             TV   !             f  !             p  !             H                !             d  !             4     CI                !             v  "             0   p  !             !               ! 
            0   h%	%	!                             p   P                   8  4t             ,     @4             Vj-                %                _             b  S                                    X         P      <^ L] \^ \ D] ] ] 0^ ] 4^ L^ \] |^ \ ] \     \ ] 0] ^ ] H] X^ \ ] \ ^ ] \ \ 4] T] ^ $] ] ] p] ^ ^ d^     ^ $7 ] ] ^ \ ] \ ] @] ^ (] ^  ^ ,^ ^ \ ] ] P^ $^ ] ] |] l^ \ ^ <] ] \ 8] \     ] ^ \ \ \      X         P    ?b		 x	 $	 	 	 4	 l	 	 б	 	 |	 	 \	 Ȱ	 	 	     	 	 0	 `	 4	 ȱ	 L	 ,	 	  	 	 <	 t	 	 	 	 0	 	 	 ,	 	 p	 X	 	     	 	 	 H	 	 H	 <	 ,	 	 X	 @	 	 T	 	 4	 L	 	 	 ذ	 l	 ԰	 Ա	 	 $	 	 L	 P	 	 	 	 0	 	     	 	 	 P	 	 H!&	             :  $             $  k                                    f)                !             L   	             $   %             8   
   y             <               F               l6*             4             >I                G               3             \  ,                4  a                f   2                {                            N               6                t             \     
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                 h  +              .   F                              '                                 !              n                   &   $                            `                                                                    (  T              (                 `                r                F                                    ,                               X  J                                  "                                             j                                              Z                f· X         P   	Dt t t u t u 8v ,v Lv t hu tu  u t t t     u Hu u Du u u v  u , 8u t u tv u @v t t u 4v u t Xt v u     pt u u `t t dt t t u 0u u @u u t t $u u v pv Tv Pv tt <u u t t `u u \u 0v t hv     dv ,u Xu u v      
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  ^ p    ] D<      T        p ; @< <  ^ ^   H<   ^  X< ; t  4   < ;   ^       (< <  L<  l< `< ; ;  <  ^  T< < \ ;  h] ^ h   x
   
  ]         \ $< 4
 _               "{                S             h  f  1A             ;A                    @             `     @               AA             tA             2l   @                A             8d   @               )                0A               *A                n  )             L               <6                              8:               m             zn                             B
               t   X    X         P   $ z x 8z z Dz  xy z y @y y 0y x <y y Hy     x z y (y y y `z z y z z 4z pz hy y y y \z z  y y y Xz y     y x z x tz ,z z y y z 4y <z lz (z  z z 8y z y Py py y z ,y `y dz z z y y x |z     z z hz z y    +}                  ¦              f                    t                            v̑              6  6f                 j               ϛ             8n             jr                                           b  }             R   
                   * X         P   H	p  Ի 0   H  \  X   d (      8   к h   T  8  ,  ` L < < P  H     l      $  Ȼ  <      D p D    l 8 ̻  Ժ      T ( x         x X 4  ` <  { X         P      p	 	 $	 	 	 	 ̃	 Ȅ	 Ѓ	 	 (	  	 |	 x	 	 0	     	 	 ԃ	 	 ,	 `	 ܄	 Ԅ	 	 	 Ȃ	 ȃ	  	 	 X	 	 l	 	 	 d	 8	 h	 	 ą	     |	 	 4	 	 0	 	  	 	 	 <	 l	 	 	 	 	 	 Ѕ	 	 ؄	 t	 	 	 	 	 ̄	 	 	 	 X	 H	 	 	     	 	 	 ,	 	    _ X         P   0	  x ġ  p  8 (    ܡ  x       p `   8 |     $ T   $  0 t P  Ġ @ H ` Ƞ     ԡ   T     p ̠    ȡ  <  , 4  |  X  `   L ؠ    t     t X  8[ T 80		                $   W                             L                   t             ؓ             2   :              r     p                            V  r                 c  X         P        \ d6   Ĳ    |    l        h,  H   <-    < <  x X  X  T           !  (    $ T  t "      ,  ı        p D      4-          81	                          3                HҎ             "   Ў                            Z  ˎ             <   n  4I                             f
  ݇                ܎             (   X         P      X  L       |  0 4   @     <    P      0 8       4 | L  p        , 8  $        h     T  D   L   P   (   p <     ` \        X         P        P Dm l  m m  @ ܂ p l m       p m m @0 \  t m Xm m       m Pn   n ` Tl m l      4 h  m  Hm n l lm  $m `m ,m Є      (l m   dm  \m X Lm   h  m      m  x < G  !                v              p                              F.  ,                 |                                                                   Q( X         P   (k1	 \ @  \  D ` ؜  |            H   p t  ܛ      Ȝ    Ԝ  ܜ   T              , t ě  h 0  ԛ x    L  < ̛ x  L | Л  T   D H       $ h     c X         P   D   p     D    H          d  d T  8    X  < \ t l                  L       0 T P      t   $      H P         (    k X         P   z1		 	 	 	 8	 	 |	 	 	 	 \	 L	 <	 	 	 |	     	 `	 	 	 	 P	  	 	 	 	 (	 	 d	 	 	 |	 p	 4	 	 	 	 	 	 	      	 	  	 d	 	 	 $	 D	 	 t	 	 	 	 	 	 	 T	 @	 	 	 x	 	 	 	 	 X	 `	 	 P	 	 	 h	     l	  	 ,	 	 x	     X         P   1	 t  u 8j  4   j ds t s  t s ,t     d s xt  Ts    j <t  D 4s h 4 s Xs  ts  s ,  t Lk     ti ( s 0t s  8  s  s s t s `   x dj  l t @t Xj  s s j <j s  tt     Q $ pt s                                  P  7'             "    ³ 
            4  ;o     X         P   % <i j i (i j xi i (k Xi j j i $k ,k i $j     ,i j j @i i i j 8. j j k j  k i i ti pi 8j Tj j i j i j     j i j dj i i j 4i |j j i i i j i Pj j Lj i i j i (j j tj j `i pj lj i xj i     |i i k  i Xj     5             ~  b               ||f  X         P       0 @ ب D   h  D  ܩ  ,       d T X |  t  0 x ` H \ T p Ĩ l L     <  P      ĩ h            Щ ` x  ( x    P   4 ,    Ш       ̨ Ȩ   |     =              
      @             ~               N   Z.               k                W                            
   d  Z             6    X         P    8F E `F ,G (G  G XG $F E $G E F 8G E F TG     E hG F HG E 4G F F lG PF G HF E G \F F G F F E E hF G G     @F `G |G tF F G G \G G E F PG F  G @G G TF F E F dG G G  F xF E E F F F F     G  F E G 0G @ ?N X         P   (2	؆  h ؅  ܅ (   d  ̅ T  |      ܄  Ԇ    ȅ   \ \    p ą 4 < 4     h       Є    | p H  x @  4 `   0   8  Ԅ l   H    @  Ȅ  8            (2	o              
                 V  7                X         P   $ hj Dj <k k k lk \j <j i j j Hk j i 0j j     k i  k k j 0  j k Xj i Lj 4j `j Dk j i dj j i k  j Tj j hk     j k k j j j |k k k 0k j k k j 4k Tk i k tj Pj Pk i \k j Lk i ,j i i i pj dk     j i Hj (j i    )             
   ߐ             L  \U 
            `          ? X         P    ؂  x ,   ă    P 0 ( ؃  8      Ă |   Ȃ @     t   0        ܃ ,       \  |   8 L  h x $    4 h \   p      T   Ђ  , Ԃ     ` @ X      b X         P   @83	 ,   X   Խ (  8   @       d P  H    x  |   ܿ  8   t     `           L  <   `  \ ,   4  X l  T    ܾ   Ƚ  м @ $        `   ļ (?3	) X         P   p  H   h <       L d D       x   8    t  x  4     l  `    t           $  <  T 8 @ X    , ( \  H  p  0      0     x  \  l                  t  z                o              n  X  
            ;o    o              d  4              v              z  : X         P       x d    @ ,    `   L        ( , ` H  H  h      p 4 d     P  |        8         (    8   p    $    <          l     `@ ` X         P           (       t           X    P  x 4 4   H   ,     l P  d      ` H    T x |     D    h     | @      8        X L @       X         P          8  l @  |    L      t           ,  \   b  d D    \     d   T        (   H         X        8    X   `  4   $ ` l        < 4 ,      x  0          L    3	@ X         P   83	` c c 4d b c c d c d d d b td d e     d ,c tf d d |d b b c d 0d e b a b c d b hc `d d `c de b     4c Lb Dd c c Dc c b d Xb <e a Hb c d Hd c c     b Td c b c b xc e tc  b a a b     c a d c c     j X         P    * @+ *  + + * l, * + *  @         0 + t  , t,   + h |, , + + f  * `+ * H  * D*       *  , 4+ P +  |+  +  * ) T +  , @   d L l* + 0, + < * * * P +       * + + +  h3	 X         P      ] \ @] h^ ]  ^ ^ \ 4] D^ P^ ] X] ^ \ P]     \ ] t] X^ \ ^ \ \ \^ \ ] <^ ,] ^ ]  ] ] \ L] ] ] ] ] ^     ] d] ] \ (^ ^ ^ ] 8^ ] x] \ `] ] ^ p] ,^ ] ] ^ ] ] d^ ^ $^ L^ \ \ p^ ] L l^     ^ \ ]  ^ ^     X         P   tRH	} t} | @} $| {  } | } { { `| { { 4| |     | } | { } | \} ض p| | } { { | | | | l} { H} } } P} {     | z | 0| |  } | { |} | t| } l| | d} { || { | { } x| X} {  |  | | } } | } L}     } D} | { |                  n  	 X         P   Y L     p      ( 4         @   8  (   ,    X    $     D h      x  L    L  D D   8               x  T      ( 0         4 8 <  X         P   3	@|  } | | { { } 4| | { `| 8| | h} { |     } } { | d} | \}  | } { } l| p| } } | 8} H| | `} t| $} |      } | } x} { } } } | @} | D} } { (| | | } | }  | 0| } ,} |  } || 4} | P} | T}     | <} { } X} 3	 X         P      G    4 0    @    5 hU 4     p 6 & S l* ` h H P 6  \O @     PO  б   D  5       R  H  ̇ X  $ 46 ر ȱ   d X 4     T   L5   5  L  @       LO  L  R     m X         P      N	 P	 TP	 `P	 M	 0P	 O	 P	 P	 O	 O	 |O	 HO	 O	 hP	 X	     tO	 P	 O	 Q	 ,P	 P	 N	 N	 O	 P	 lQ	 P	 N	 pP	 XO	 P	 @O	 P	 N	 O	 O	 O	 P	 P	     LP	 DP	 \P	 P	 N	 |P	 O	 O	 N	 O	 pO	 O	 O	 TO	 xP	 P	 P	 P	 lP	 P	 (P	 P	 LO	 O	 O	 O	 N	 <O	 N	 8O	 O	 lO	     HP	 dP	 PP	 P	 O	    ^ X         P   3	 |   p   4   \          d  (  H  L \    P    X | $ 8 8  P  4 p     @ ` `  X  ,  0  < $ @ T   ` T  L   <        h H       l d T      X         P   .	̛ ԛ d      $ X   T   l     t   Л L F   h  p `     H < h   \  <       ,  ě  ̜  (    L   Ԝ      D    ( 0 D Ĝ  $ 8  ؛      d 8   3	                              T X         P   L	t      8     L   T t         | $   `         4   L  l x @          (     0    |   0 p     e
   P <           d  D                (                  H                                                           َ             ^  ~ڎ             B   P               6                      
            L  ;o    
             ގ                d   ǎ                ,                             2                I                *             R     Ď               &                L  4                          i                   /                   !             @  ~             R   F                               |               >     gI                             :                             `6                                "   @               "   I                                          f               
   7             z  ;J                                  *               v0   6             4   Ŏ                                p                             <                 -             :  |Ǝ                 i                .               Z9                 X  ߎ                F  $               >sD                                                                    J                +                (                   ώ                 )                              n                  L  I                Î               hԎ             0                @               2                          h  8                          ؎             0   Z               
T   ]               V(]             xL\               $   ]                  q\             D  1]                \                \             x     \                \                  \                   ]                  ]                F\             (                   \             *\                *#]             X  ]               B\               j                   ]             P\             .   \                ")                   \                \             0  \             V  ~\                *c]                B\             ":   \               ~  c             Z\             8
]                ]               \             6*]                ]                0]             J   A                \             4  H                \                ]             ]             l  v\             Z   \             >  \               ]             v   ]             (\                 U             \    ;             (   V    X         P      Hm m l m m l l ll 0l <m m Tl n hm (n m     (m m ,n m l m dl Lm l n pl l (l m l m 8l  m $l m l 4n  m      l m k l Xm l $n Hl 0m <l m |m l m l pm 0n 4m m l Xl l m l m l Ll <n  m l m m     m 8m n ,l n P  X         P                   ܞ x  Ȟ       X H      ( l   ğ  8 Ԟ ؞ 8    l $     l | ̝  4 D О \  h | (   ܝ T h  L ` L t T    Н p ԝ    P       $ ,  x25	~              
   Jk              t     ߑ              n  (                9                  ta                 g: X         P   X	|/ 0 80 l/ 8/ / x/ 0 H0 / / 0 0 / 0 4/     / P0 / / \/ 0 0 0 / / / 0 0 $0 / / . / 00 / / / / t/     0 / @/ . / / |0 0 / 0 . P/ . . (/ 40 / / x0 0 T/ D0 \0 . 0 / @0 @ / t0 0 L/     ,/ $/ / 0 .                                 T               ~L  E             H                g               b                I             _             B                 d                K             d  4   a             ^  D                (   ݐ             &   D             L               ^     *             r  I                S                n                   f             B    !             j`             J   bJ             H   V             0                  Q             Z  `  %             `                              @                  b   ʓ               0   ȓ               .   Ɠ                          V   ғ             ,  v                   ד             T   Г             >               Fx  7d  
            r  ;o    ɓ             f                                lHJ             3                  |ߓ             6   @             X                  J
x                                               |               !               Փ             T                  Ó             d             ē             ,0               :<                            (                                l  A                             ^             p  j               V                    ϓ                                   Sj                   ̓             N    ԓ                            l    
            l  ;o                                ~ݓ             Z                z               ,   Ǔ             *                   
                                z  {D                                 x)                                t               Pޓ                :             L                p  VI                                  ^͓             f8               6             L             @   ۓ             H   $              >   #                                              P                            \                                >                   zR5             $  Z5               P5               5             >  >  -             Hb-                 s                 x                 ^  U                H                                    6a              Y                :>              j     i                                j   Z X         P        ,        <     0 L      T   x  H  H      ` d  8 4 <  H (  
     X P  L P h X h   @ ȉ 4  $ ؉  , t 8 P Ԉ ܈ 8 T   0 ԉ  ( p     @ Љ  $ ؈ u
 x X         P       L{ | z 0| h{ { t{ @| z | z |{ <| z z {     4{ | `| y z $| tz | t| | | lz { { 4| { H{ P{ { z d| z X| z     z \| { | z \{ <{ D| { { { 0{ ({ | z z hz z { { { X{ {  | ,{ l{ z { { { z |z     | @{ p| z { #6	 X         P   A	d ؆  Ї T X  |  \      t     І  P h p  $   0   `    ȇ l  `           l P <  H  x  D  Ȇ d  8          p Ć P   l h  X     $    L <  w X         P   (F"	    ,   h 4    @           |  d X       p |        x < 0      \ ( L T p    t       X   x Pt   @  `     D           d      X         P   	dD D HE D @D 8D `D @E D C |E <E C |C |D E     D  D C DD D D \E D E 4E D LD PD D $E PE C D C i D D D  E     E C D D LE xC C E <D pE C D D (E C tC DE C lE C ,E 4D HD TD E TE D xE E C E D     lD 8E C `E C    * X         P       ȩ  Ԩ   h D ` T 4  d  p      T   ܨ   Ш 8 ,           `   l ,     x H \   |   ܩ L 0 X 0 t p X <  @  Ȩ  Щ  t t h   ̨ L        l    `]6	                 ʛ             ,      O             >  ]             2>  c             H                >b             Pb                  ,˛             "               ֛             Z                    "   ڛ               ț               ̛                                :|                                b                  KJ             	   [                 j             @F   d             DT             "   ۛ                                H  j             J                  p)                   ћ                ƛ             ~z                                                            r  k               p                               I                   e             ܑ                                 Z                    Y               u                n                B                   0ě                ś             B   Л                f  2I                a             zқ               L  s)                Û             8  h                x  Ǜ             T    J                X             Di               $             vn  x             ~             z             <                  H5 
            `  ;o    R                               I                _             Hכ             p^             >S               <^)                g             n  ͛                  ^             2|               Z                          b                m             br  i             :   \Φ 
            Z   D;o    N             6H                          vX               :                               h                   `                j               $   |             D  g                             j             l  2   9                          F   `q             ;               ,             
   vC               D             6Q               A             F  
                G             tZ               ,4                 $             XbI             &   2             `     #             ?             z  A                V               o             z^  )             \   m                   0             h               6  r             d  f  =             d               K             :   Z                            r  b             8                                *               Z             D                 a                |6                r   H                             |                               .                   (                -             B   P                 x             D    4             Z  P]               &             n  <                  )                   ~               L             6   L             R             0   P0)                    O             P             r  <               V܉                ϑ                 j              j  ]                %V              d  <*                H*             44   U*             xh*             (  $               *               t/*             r  $*             H                   {*             @  *                                1   ]*             I                \*               c*             d   2*               J   i                    n*             ,.*               >*               J*               r*             *             l  x*             B  *             X  y*             \  C*             `J                    %*             A                  K             j  "             p  4                \               ~             h  ,             R  N             6   *             w             B                                   jJ                Q             R  5             JM             @               
  A               I             &  6             .P_             (  4   3             "  d   Dy                             (                                   ! 
            0      ;o    (                                               "                                X   8                                               v             T  a                 #             6  }                  k             \  R             H                F               L             \  J             .                            ^  "/             x   i             f  !                 ;                          f                   ,               FbD                                B               B^Ȧ             |               5             |  ۦ                                          $      3             v  Ϧ             6   X*             t  n               ~  C                                 ˦                            *                \    Ʀ                             1               rJ                Ǧ             J  Ӧ                            ,   4                 "	               צ             ^$               -             p     .                 }I                ڦ                            ~  >                P  ɦ                (                              \   H                   ?             jf                       i                                 X  >æ                                         L   J!             v                               .O 
            ;o    ֦                p                            N   RI                                                R                 v   Ѧ             d   ʦ                                                             ~                 p             ~
                  ٦             6   X                            d  ݦ             i                                bn                  <                            x             ̦             B             &                v  8   %             r  '                            :   B X         P       l  d   D l  L   , 0 <      l      X 4     , p p T  8 |          |            d    D t 0 x x L $ P p   t    0 (      h   @ f              8  4T X         P   ]	   p P    ̃  <  x	    $      L  $   8  \ Ȁ   @ $  H Ā   4 ` o ́ h h        ܁ ā (      p p | t 8  L   t d   , X (   <  Ԁ              J_ X         P   Q   p  D  h x  ؉ 4 < (  p            8  0 T   Ȋ $    l   Ԋ   T 0 h d       ԋ  l   ԉ   P   Љ  ,             $ < ȉ  4 ؈ |       ܉ D  1 3 X         P   (	w v w v Hx $w v  x w v 0w w w x w x     4x w v Lx w xx x w v w |x `w y u Dx w x w x x Tx w x \x     (x dw x  w x (w 4w w <w x xw x x x  w x Hw v px |w x $x Xw w Lw w hw <x w 8x x w     v ty lx lw ,w <  ' X         P      ^
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    )             n  A             n   v                                L             8bH                g             Z                       T             J  O             J`             x  x  9               d             #                            n  "R             `  Q                bt             N   >                                           A             |  4                :   (2             6   P                              6                )                               b             F+                                                b,j                             Zc1             *L  l               X             ^             *   c             dZ             |  uw                                                  f             V  g                                               U             (  w               "                (                                 i                              H             G               .j                J             ,   \                            R  o               &               @             .8               "   i                               4             Z   < 
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 d9	X X         P   t	    $ <  x H t 8 p  L   T         L     (            0 D  X           | 0   @ ,   x , 0 $   P   D l              d ( `    ˸ X         P   9	`b b pa a  : a : xb b  b lb a a a b     TZ a b |b da a ; @_ a a La tb a Tb : a : ( (` @b a a b b     Db a b ` ,n ` Ha a ,b a Pa b |a : db a b ( pb a : b Xa b 0a $b `a _ b b ha a     a a a 8b b                  H                             4                :             f                                               (   
            T   P9	_             Z_               _                _                `                  _               _               &   ^x                   q_                 _               _             p   `                Pi                `                  `             B_             v>D                    _             B  )                _             (  *  _                ._                  _             Z  
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   _                 _             6)`             X_                  _             .  `               _                  _             (  _             l_             _             _             	`             ~  p_                `             L  `             .
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            "  j        gA             (4  J                   A             D  *A               A             JjA             *  8A             ZZ             	   PA               eA                ,A               BA               ^  qA             0  iA             B	  bA             *  D+A             |  MA                 )A                JA                "A                  A             2   x   NA             %K             QA               LA             P                	   7A             8TA                A               	A                WA             $A             >  ZA             h                     A             r   A               PA               )                nA               A             \  [A             X  A               fHA                   hA             l"zA             H  {A             wA             h     rA 
                     A             <`               >  1             	  x X         P   :	 d x < D  t \  $  X  h H $     į     ̯     P  T   8  ̮     x Ԯ          @  l \ ( d   ԯ  p   | L D  0   8   Ȯ     T ,      ,   ,                   r   :%s X         P   
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             Ny             8               4  d             ^   vi             b               
   n             V                hI                                                .             X             x               @                                     *   +             (z                                o                          b                    g                                          `   ^                                                                (   A                                X                                 <               *
                               l                              x                b               J                                                  k   X         P   $     P  h ( c ș     \ ,       l      4  < ̙  $ H @   t                  4 d  0 (     @  p  ę D $    t К  L       Ț  p X                   (   6   
            h;o     X         P   &   ! <! P  !      !  !  t L   !           P!    @!    ! h     ,   $       H      4!   D          \  p      D!         $! l!           l   T! @  t! | !  ! 8  <        H!    p                n  6) X         P      X       x $ H     D `          <  p     X  4  @ L `   (   $  H     |  d  D  @  (             \   P   x         0 T    l ^ X         P   lb	  L       H 8          ̑   H  Ȓ  p T    ,   $ ؑ   X  L   |     X ȑ P    4   t  Ē đ  ,  t  p     P  ܒ |   (  ̒      T   @ x;	             `   x             &                H                                     f                                *                F  y(                             $|                              l                                 t                                "                 ,                                                oD             
                  l                 *                           P                              >                                  
   y             t               T  
                             <               d             dh  8                             j                                                F  >                             d   C                             h               :             WD                             Z                             >                                                          ~             &               F                                    )                                                         N               &                    }             F               v                            h                                              &   "j                                   XC                             X   ~             Z   >             z  .               2             z   `_ 
            tT                       f               Z                              *                            @                            Z   N                                            0>               :               H                *                                               (                  \                                  (                                                               <                J  mJ                	                H   
               :                                                 *             &                                                 8                z     !I                             F                >   6)                             H                            >                  :             H             4             
F                L     H                                  @i                             0               <                               
F                            2                N             V     A                                     A                                	                                                              f                               *                ^             >  R                ha                             B                          F7j                          -                  B                              d                            % X         P   p@<	 @   X |  t d , 4 t                t 0  P   @ <   ( 4  D P        L p  < X    8  `    ` d  x     ` $      (  , h     X   T                   B  @ 
            
          Ջ                                                              0                 V                                            T     I                             \   H                j             L               \   v             2             @             zOI                                
               
   u                            d               N               R
               r             t               B   
   n             L                  ~                b   t                            2  v                                             Z                                                           h             .                               V   i                                |                                  l             R  w)                          o                })                                                   !                                                             0                                \                &                     y                  i                             :               ``               d  n                              (   p                             
              ;o                 f                b               N                            j             6                 z                          x  x             b
                              K             *  \             j  .             \  ,             P                 <  J                A             b             v   h               i             *  j=             F  2             R     	             A                m             "   C               J                  p%                             "'             `  "             \   k             *             $             >  2             ^Jl                   7             .  *               I             (                   *                  '             \  C                   U             @   x             R                  I                h             F   x                ?             2             :  P             f   W                            @   9j                    T             l   4w                5             d6  O             N-                 ^                                              ,[)                   g               G             &   &                2   H                f               )             vd             J                             r             @]             w                n               D   !               9                            ;                 p               (               J   t                                 $                J             J   >             *  \                x             6   4             I                            /               D               Ro             :   "   u                               ~L             x   Z                             N                                 *   
            *;o                                                N                                *                   x             @                               4                @             0                            &                                 .                            :             `                F               &                                             >                               0                            :                  
j                                 F                2             T               0             \J                          B                                   .                  0             Z                                                                   |     rf                                          2  (                                                v  )                                             $  z               J   "                               0                                                L                 *(                                nD                              L                               F                t             6  A                                 Z                  R                H                &                  @                            <  t             (                      :   X         P           T 8   L    l p X   ,      \   l  h D    đ ȑ     X P 4 | x 0 Ȓ     P 4   ̒ h ܑ Ē ( $ , $  L D ԑ H  $ (   L x ( ܒ  8 `   H      p < d 4                      u X         P   Q  ,S |S S U S T DS S T T S U T S S TT     U T S 0T TV T S S R T T 0S T pT XS R S T S T T S T (U     pS R dS T T T S (S  U LT @T xS dT S U \S V T T tT (T R |T S 4T @U S T R  S S U     T `S T S R    N~ X         P          \ P ,  `    $ , l D Ș      ,  f < ܘ  4 l  Ę       T H 0    ̙ t  t     \  | @ x    D 8   X     ̘ d ԙ   h  @ 8 Й L 0    P      ؙ ؘ x   >	3             l  4               
  (                    3             3               j3             V  h3             4                3               4             3                (  3             r   8  3             63             4                3             *  3                 )                3             J     4               
4             0X   3             3             ^   3             B   4             n     4               &4                                                             @   ^               H                                  *                                  )                                       2  $             &"               $  F                p)                /             b               ,                               rL               \               .  
               ^  H                .                          ~               h   T#             F  B                 `(                                |   8d                                ^              r                            4   l             x                  nV               <  H                                  C             
             h                                 Pj                             : 
            
;o                 dv               B                ~    =                                          
   (                *                                  .                                  T   'x                             8   (   e(                              ^                            
  `               T  I                                                4                T   X             f               H                                            (                >   w                               i                                 f                                               <  "                             b               i               6   N                            n             :               t                                                >b                                  n   ^  J             $                h  8               R                                                                            W             2                     s             D               `X             `               V                  r5j                c             ~x                          R    _               X                   Z             P   @                   C                v             L   d               T                    y             (   V             "               N   |                                          8  RY                          R               )                               X               \                 6               r                                              d                                                $  \             ,                            8                                       }J                   k                          LZ                &  w                            `    H                                      l             e             )                             n             (                 *                                     I                   {             0   J  p             :   ,                ~             T             P  A                O                          ,   P               4   f             p  M             &     U             r   |                *   Yg             X   g             :                               f    i             x                     |             n               \                               .               >  m                6                  I                                               |6               "  F                             T   b                                 ,   J             4                e               ,  t                            p   2                            D                                              X                              8                              X                             p|                              D             (   v             b   N             6   ,                @@             j             >   Hu             :  `   V)                                               p               C                                  h                              ,               n             d               X                                                 w             N  h             pj             |                d                                            2   l             H   le             T   f             z
               "                             x                R               @  H   k             p               
j%)                    {             "               r  L             h   N                                          Xb               *   x{             \   q{               e{             T   (                {                 {             {             .               D                6                               .b                              j                             `   F               i             	                `               B                  Z   (                                                              H  J                                I                *                               i                                (                Z    (D                                                 	             4                               p                                   I                                                             
               ;o                              N                 6                ,                                 w                  2             ,               P   %             z                               T               '                             L               
4                                           6   (   I                (                  N             <             `                               $                z                                             n               *                0                     1               |             J  G             ^               R  0             &  <             x   0(                                  *A                               6-             pp               d             6   04                t             |               r  /             |  J                J             X  3             T  L                lv                            x                   h4               .  >               ,                  )                +                 8   C               I                                               
               v             Z             f                             
  X             8  X$             L   v             t                                ^                                               t                 n               p                   Ȳ             j     t             k                Ų             v                                  β             `   .  ܲ                          "   4               P                  l  ̲             
                   ߲             ~  ײ                                B               l  
                                                             f                               v               4   c             ^  kI             
                {(                   d             
   %U 
              ;o    ϲ                `                             r  (                  Ͳ             d  Ӳ             d               d    ò                             |                                  F  -             ^                .                                   C                                >                =                             	                t  `Բ             ղ             p                   iJ                               )                                (d  I                                               ˲             z                 D             Z                ²               ֲ                            x  	                                              <                            
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   o                O                                         h   w             J"                                 S                 /             ZW               $                               D              4~             lP             j2  )                 T               |             d                 (  m               L                                                 5             h  t                 @  E 
            \  ^                       T               H                               [                                              L                  i                                                            L             (                            H                4               0                  6   w                             n               <     "             R   )             F               `               z  P                                            lT   (                              "                \                 l                   f               X  &             lt   Y X         P       0 H  ̍ D       ، (       ؋ x  P   @ D L    |       d   ̋ $      H  ؍   Ԍ p   Ћ ȋ Ќ Ȍ ̌ @ p      ܍  \ č  ܌ ( <    ܋     \ t                      <                ; X         P         p   L   ' l (  < |  ` H      8 <  L       | 4  t @      d  d      D 4  T    X   l       0 h  P   t H t d h  ,   \     p         C X         P   MD	`	 	  l	 X T
  x
 	  P x	  
 t	 	 |
        	 
 d	 	 \
 	  X
 	 	  8	  ,
 	 |	 	 	 	 x 	     4
  p	 
  	 (	 	 	   	  0
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 <	  |  	 \	 d
 $	 p P
 	 
 X	  	      	 4	  (
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            N   ;o                 T  	             :   fJ                                n                            0  ,                               dN               R   D               H             L  8                            `  Z   )             6  `                                Z                          !             ~                 x   w X         P   (E	e Hf f e  e e e e f d f d d f `f 8f     Xe  f d Df f f f d d e he tf d e e e e d 4e e e f f e     Pe \e e e Le  e f f f f e d @e f  X f e $f  f e e te e @f d Lf f df f e xf e     f 0f e d f  ˸n               b  `             .                ,                  l             D                P(                	   s                          d               Z                   g             0  d             H   `)                                '             O             t  +                                            ~  r  y             *   I                >                             J  x                                               h(                P             \   nE             z  A                G             n   U               S             W             `  rl             \~ X         P    <  4    \  P L $   @       l     @   `  t  h             `        <      t      (  ( H `  \  P 8   L  X  t        ,   =                X         P      \ 4  Ђ    ԃ h D 0    l       `  ȃ ؃   0 8 ܃   8     P     @   D       |  H Ԃ X p Ѓ l H       ؂       L (  d d $ <       ̂        T X         P   PGE	` ` ` `b lb  b Ta  a ` a Hb b a a Ha (a     ha D` a a a Pa a ` ` ta a ` a ` ` a t` X` a $b  a ` ` &     @b a @` Da ` ` a ,b ` a `a ` a h` Lb Tb ` la 0b H` a Xa ` a ` b da xa ` ` a a     x` p` b a <b     X         P     T       7 \  L L X  P      l ( x  p        8  t   , d   X p8 <          ` <  L7 $    d 4 ( D  x7  8  |  x              0 `       X         P   	tc D x  x $ z z Hy  H \ V y 2 y     p &  z \ @  lU (  L 4  dy Ц   U y < U   z |x       L 8{ Xz (y  W x \ z = y ț X y  8 z L  xy < | Lz  t Z x   |# 8y y      T z ty (= hUE	L             4      { X         P   `D     d  Td          l       p @ T d    t  `           x t      p      8 ` x X  h    T P    < h   @   T          4 X  D \                 J   Z             6   A                   c                $   Dj                             h   |             V  Qw                                                      _             h  HD                                      S                               v               q                  I                X             N                              0   $                (ZY             8  d             <                                 d  i                m                                                         J               @                               <   h             t             ,  0                *   
             .               &  T               x             dg                            J             D                &   0                                            0  R             J                2   `               p  '             $               R   L                h               C                             p(                                                                *                             4                                                  F             MJ                             *   #J                                  F                               f                \               l  1j                             
                          ,               <                      C                                                     #                            ^             0  _                 ^               4   D                   	_             j_             4  ^             ^               <A                ^                6_             @  ^             "   ^                ^                ^             4   _             0                               V  i                @                          
   ]             DA                             .                                   H)                                [                             .                ,                               )                )                                                |  O                             (  3j                                ,  Z                             4                            D                               (  a             0  
   =             *  z                          $   X                  ~             <                 &               N                >   ?             &  ,                 Ǒ                                          (               r  3                Z2 
               @           0- X         P   T	  D   l      T 8  X   $   t  (          D   l       \     $   H   (     \                       <   $   0  8   t @     d  L       4       T        X     0 G	!             "             D  6!             !             `z   !             !             !             *   "             !             !                  "               (                   !             ,!               !                b                !             "             )                -   !             A                   "             !                !             v!             0   <  !             `   !                  "               C                !             8   0   "             .   *   !             !                <  !               "             "   X  !             !             n     !             n   !             H                   !             D   "               !             z  !             0     "             @  f!             :  "             &   !                !             R   @   "               .  !             lN             %             %             x(  %                   %             6%             &   %             :   6  %             i                    %               %             %                 %               |%             x%               %             %               %                  %                %             .   ,  %             %                ~%               (                %             P  %             (  {%             l   n%             t     %             n  p                %             j   r  s%             %             P  R%               z%             :%                  %               DH                %                 %             0      %               %                 J             	   	   w%             L   H  B)                %               %                J                             B   %               V|%                          C                W             f\               4             V  M                 <                2                                @                               L             
     i                                  F               p)                                                 t  z             64             R                 `             L                  u                               6.   y                              Z               V6                             n  ;              
   Zm               2             2<             L                                                |Xn                          6  %             F  t                >d             0  a                             f  'J                             "     \             |             V   l)                g               Fw               l                                              N  H                                                                                    u)                r             V  w                             T                6                            F             d                  "     ~ 
                      t*             o*                               *                bI                   W*               rG*                  3*                *             " *             F  *             t  *                 *             ,h  Z*             :  $   *             P*               E*                4*                e*             &   z9*             :  v                *             n(                   *               jwJ                *             ~*             <,~I             $   b*             ^  H                   l*             P   g*               N   *             t   O*             `  V  )J             	   	   F*             r*             J   8*                *                   ,*                >   *               '*               5*             d   9I                `*               >*               h   7*               r(*               |                *             Z  V*             :   dS*                }*             @*             4    L*             $  *             :   2   Q*             Z  N*             n  H                j*             T  d*             t               (                    7 
                  + 
            p  ;o                 v               Fo X         P          `     @  0   L l     h H     ؔ   4 Ė  \ < , Ԗ d   ؖ ĕ | P @       $ x   h t    d ,   `    P   (   T  0 ̕   ȕ ܖ      ̖  l                   F                C             $   "             \   ͞             P               (  I                               5               ZC                             h@                                    ў               $               4               ޞ               V               @               @                            <  õ 
               ;o                 "   ٞ             7               @   *               R  (                ɞ             "   1             r  t(                                             pJ                  ܞ                               b                             :                B   -               v               v             r   v             ~  Bw             4  "v             rE 
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      {             *{               \{             "  {                  {             {               h{             r|               ZJ                {             
L{             J     {             "|             
     {               &{             8{               {             J{                  {             Bf  {             p  m             (  {             ,{             ~|             {             V  %|             @  
|               {             L  {             6     A                    {               X{             D    {             
6                {               $   {             V  E)                {               :             x  +j                :             f  :             @  P:               ::             2  I                r:             \0  :               {:             6  :             H    :             &   b:             t  l  :                  o:                :                 :             8   :             r   :             f:             Z  :                H                :             :               :                  J                :             (  :               :                :             bt  :             :             :               w:               :             4  :             `:             8  :                (                p:             <   ::             :             d:                0   :                :             Nq:             R:               V:             t  j:             l   :               :             n.  :                 F   :             
  :             fZ  ~:               8:             j   :               r   :                t:               hJ                :             y:             :               :             :   6   z:               <  :             @   I             	   	   :             6:             H  (   :             R   :               :                ^                 :             `   :               T   :             `:               &             p   @'             (                   &             ^   J'               \J                   &             t  H'             P  X  &             V\  &             N  D'             :   Z&                &               &               4;'             x  !J                &             &               6'                (J                   &                @)'               "H                -'             6  &                '               &               5'             Pl  '             X  "   '             d  &             &                F'             '               '             <`&             L  &             ,   H                   &             \&               &             <   (    '             j  A'                T'             2'             '             @   &             j  j   '               &                 &                               &               '             6   x'                /'             t8  }D                   &             d    I                &               &                 &               :'               &             H@'               &             Z  X   '             +'                 '             t   '             j6C'             8  . X         P   g	
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                  P                             B  D             )               `)                !                             ^  )                   `                a               Z  xa                6                @                            6  pK                Z                              P   tf                                             x~  %D                               :             V     [                                            &Q             
   1                 l  ^             .                p  F             `  L  @                 !A             $   @             x@             PA             N,A             n  q             BA             :  @               A             .   @             N   @             2     @             $A               I                A             `t9A             6   x@             D   @               @             z     @                "A             B  A             j  A             v  'A                d  @                  @               A             D?A             4     A             L  @             &  CA             `@             Z(                   @               
A             0   4   )             @               A             t  A                  2A             L@             t   @               A             h@             2  A               I                   @             XD  6A             d@             <   >   A             7)                 A               L=A             T@                .A             Z   H   4A               <@             &     A             l  A             0   l  8A             D@                 @             x     A             ^     @             8   J  D                A             3A             xb@               j  @             8@             ,~>A                             N                "   A                                                  BH                <             ~-                  y             H   U             ^  &             RX                               V             (                Z             D                ,                  6             R             ,?D                   x                I                 ^             X    m                           ,  M               *  II                   v             ,  &)                e             L  F               z             .               b:               w               @                               3               N             L  a               ,q               ]D                             j  hi                              h                             R.               
   1                $8               ,                 l      ~                               8   (                O                                u             b                W             6b              h|                                 *                B   :   I             q                                                8^                                d              $B              D   =                              v   D                                                                "                                Z                                a              t  "                      \              p   Y                	                ֠              :                 &ʠ              >     xi                   x                                ,@                `  J              (t              8              8     $              r               0                  r  2              t   N                I              4   6                 J                     c                                $   1              V                     à                              Rj              d     ]                   ˠ              N              6                   hJߠ              $H              f  ;              f.                 D  ))                                  L+                `                 
   s              &hw              `                   ),             4   *                            D  j              >                :                                              t5              .                     >              <j                                .x                                              ^  <             &   F                  ?             N  d             j	               (                    [             V   $"             !             4  v   A                             H  K             #                <                r  6G             x                                 I                                 -                >3)                ߑ             0^J                            :                  6S             \   ^D)                             Hw                                >I                             :  L                             _   
              &   ;o                 B   >5                               &             .  b                Xt   
              j        v X         P      . 0 / 4 X/ 0 2 / 1 H0 - 01 1 d0 81 h0     . 0  1 0 - t1 . 1 0 `-  4 00 `1 H1 0 / 1 / 0 4 ,2 D/ / 2     / / @ / / 0 / 0 T/ 0 D2 0 . / - 0 / @1 x0 @0 T0 x2 $0 / 1 2 0 2 0 . 0 ,/     2  . / 2 P1 8N	0 X         P   D} b <b |b ta b tc a b |c  b a a a Xc a 8b     @b `b (c b a b b b |a b b c Tc la $c @c a c `c b Pc Xa c c     b a lc a a b da hb a b b ,c xa 4b \c a 8c xc b Ta a hc a b b Lc a tb c a  b b     \a  c pb a a  ^             \  N             \  N               N             R^  #I                N             ^   N   N             H  N             :  I                N             `  N             h  N             N               <^ 
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  
             
                  v               R                 ˨             @                   ר                                                                                 i                                                                                        
                                               h      @D                             B                >  J                                             ,                                        Ux                                *  H                               2@               D               p                T   E             >  6                             K             ~6  [             :   l             <l               r%                   &               .  a             v   Pp             X               (i                h             L   >   :             &                 F               0   F                            z   >             $|D                -             v^  v                                              ,             t                 
/                                 "x                I               R             D             l  #j                *             J   hC             X  .V             N   i             4   w                '             (   W             `%               j)                 \ X         P      s	 s	 r	 r	 ,s	 r	 Ds	 Pt	 s	 8t	 s	 pt	 t	 |t	 t	 lr	     s	 r	 r	 xt	 q	 t	 Xs	 s	 s	 s	 t	 t	 t	 t	 t	 r	 Dv	 s	 t	 `s	 s	 t	 Ts	 s	     0s	 Tt	 ht	 @s	 r	 ds	 s	 0t	 Ps	  t	 q	 t	 \t	 Ls	 s	 r	 s	 t	 tt	 i 8u	 ps	 s	 ls	 r	 Lt	 r	 s	 dt	 u	 s	 |s	     ,t	 s	 t	 r	 (t	    U             t  $U                U               7U             D   (   'U                  v                U             zU             ZZ  (                   AU               )U             lJ                0U             V   U             v    RU                U                L   U               zU             :  J                |U               EU             ~   sU               "U             
J  FU                U             &  (]U               U                 VU             U               I                U             (   U               -U             l                   <U             2U               cU             :   ;U             8U             
   >   U             J                PU             T   4U             x  $   U               U             df  P  
            "   z;o    U               \   TU               X!U             ,  (YU             $?U                QU               A                3U             `  &w                oU             h   5U             6U             V[U             0&U             U               (U             F   `U                 U               U             h   U             dJ  U               j  #U               ,U             ^Z  @U                U             Rz6j                 1U                U             Z  MU               U             "   8GU             L   U               =U                `BU               t   7J                U             8>U             x             *   +U               9               N$D                f                  s               o             
                                fD                            0   K             PK               L  HI                K             
  K             :  K               &K             N   ^   L             R	  "0L             K             Z  i                +L                  K             6H                K             `   ,d(                L             :  K             d   `   L             H                  L               L               K                 K             6  2K             .  K             p  7L                |   K                  L             Z   |  F                    L             
P   Oj                K               &   K             
	1                L             nK               &  5L             /J                2L             
p-L             K               "L             z   j  K              K             B     4L               K               K             ^@L             "      K               K             |  K             $     K 
            X           /               b              #      X         P       (K $K L $L L |L K L K L hL M K K K L     K M K J 4K HK 0L J L L pK J L K  K J lL J J K J hK L K     K 8K K J  L K (L K DL K L `L <K L K 0K 4L xL XL L L K J L L L J xK K ,L I J     J K LK L dL     $                                               P              n  K             4c X         P          t  p   d    h $ 8         (            @ l      < 0 x     p  \   ؍     t L    4    h    0   4  8 |  D          ;Q	 X         P   ,e   а   ܮ     0 |          t |  P 4 0 x h     <  Ю <  Ȯ  x  ( @ d        `     P  ̯       H İ   8 ԰     t $ @ 4 Ԯ        ,    X         P   h   (  ̢ $ (   0      p     P           L `  l  ȡ  ܢ <    T ,        x     l h   \ @ @     4   ؠ  d $ 8 Ԣ ܠ  T       ̡    ġ h _-               N                 |^                                n^             @^                             ^                dw                   t^               ^             n   ^               <^                y^               Rj                r^                D                ^               j^             ^             h<^             2  f^               ^             "  ^             L  ^             <  
   ^               T             t2~^                @^             x   ^             |   ^             ^               ^             I                   ^                 ^             N^               (^             A                ^             ^             T)                   ^             .    
            &   d;o    ^             (  ^             L|  p^               (                e^             T  ^               k^             d   
   ^             ^                  ^                ^             z  u^               ^  ^             4  ^                  }^             &  ^             JR^                  ^                   ^             n  9J                   ^             (  ^             R^                x                ^                            ^               ^                ^             L      o^                  ^                h^                (                ^             `  q^             x  (   ^             Z  6   ^                ^               ,i                ^             ^             v  p  ^               ^             ~  
   ^             ^             $:^             s^               Nw^             ^<                X                 y                W             	     d             F     a                i                   *a             Ka                TJ                   `               V8a             6  a               a             8>=a               b   a             <  oa               :a               |   (             ,   ka                 <   b)             0a                g               ]g             Ig             vg             8j   g             
   g             ji                -g             \  	g             Z   <g               ^  g             0   bg                  g             |   Vg               dwg               Cg             n)                mg                Mg             "   g             d   vg               jg                ~  eg             .  6  Jg             8Ng             x     J                   g             h6g             l  g             H   g             0g                 tg             |  Fg             ~  lg             v  6g             rg               zg             pC                Ug             0ug               A                   g                  g             b  H                   yg             g             ~Ag                  g             :  cg             0Pg             <     =g               H                 -   ag             8  Xg             2   qg                g             $   g             <   t  gg                (                sg             :  g             Rg               :ng             j   @g                  g             *g               9g                g               {g             .     ^g                r  Lg             V     {I                Wg                   Dg             J  >;j             
   g             |  g             I                g               g             8  ?g             $  }g             g             J   *)                   *g             p   <  i                pg             t  S               )T             TS             vI                T                bS               FS             "  ,S             J  J                   {             r   S             2  (                   S             Z  S               
T               Z   S              S             V   `!T             T               LD                T             *  S                T             d,)                   9T                ,B                   T               I                8T             $  )                fT             2  \S             `  4T             l  S               S               T               T               T             D   T                S               &   S             [T             ."  T               "T             fT             z   i                S             j@  #T             j   2T                 S             B   T               QD                   S               H                S             T             &   T   xS             6  T             S               0T             :@S             t  T             \   T                7T                 ~i                S               *  S             d  Z   I                   S             7  S               x   T             l  S             rb  S             S               *T                   S                DS                8                   S               &T             t  S             S                <i                   S             \              "  y                R                 :                z   Ls                                 V             \   a               a             DT  qa             p   `               (   a               |fa             T   Oa             p   
a             b  "a             F  8   sI                `             "  `                (                _a             a             >a               j`             "  T+a               a             4]a             |Ia             4  @,a             n   5a               da               3a             uD                `               a                p`             @   2   :I                `                ^a                a             x  pa                `             |   Da               Fa               V7a               ?                   La                  a             wD                <a                [a               `             ,  aa             8d  ta                 na             D   6a                 i                 a             a             >T  Ej                   Ya             r    ca             nla             ~(|J                `             d   `                (a             B   Aa                                 )a               a             4  `             ~Xa             T2a               a             "   `               `             :    Va               `             $p0o X         P   T	( , l D <   p 8 $ L, l   h      L  ` Ȣ أ | <  D 0  ȣ  d    P  |  \ T       @ \ < $ H   l   X  0   ̤ ܣ Ĥ       Ф    x t  Ȥ      H h       ll             &   l             n               n               $   n             L  i                o             8n             ,  v             *  v             x  SD                v             2  v             v             Xv             82J                v             blv             d   rv             dv             v                            v             $   R   J                w             x  l   v             v             JJ                v               v                 v             Z  v             x  v             z   Xv               v             X  w             |  v               v             +D                v             V  v                w             6                ^   vC                v               N                  *   v             @  Rw               w                2v             R   F                v                v             FO                w                Xv               z   ?j                v             G  v               i                   v             .   j                v               (   v             $D  Uj             v               v                D   I                   v             v               v             N   fw                .w             w               v                Fv                v                v             v               v               ;                v               "                "             @S             $  ZT             $                   *   T               %T             S                bS                  "               "               vL"                               {"             |   ~Yj             
   f"             ""J                   e"             f  "                T"             X  8"             Z  i                   P"                7"             "t"                l"             Q                "                  "                 O"             "             u"             4  \                   N"             4G"                d^ 
                 ;o    K" 
                    ;             $8  D                \;             `     ;             $   ;             ,             j   ;               v;                ;               D                ;             ;                A                   ;               ,                  ,             ;             b0,                 ;             2  p             *   ;             r  B                ;                ;             2J                   ;             L   w;             \   ;               'j                
,             .X  I                ;             :z  +             ;                  ,             2;               ;                d  ; 
            d6         X         P       @ ? @ 8@  @ TA 4@ @ d? @ ? ? ? dA @ ?     d@ 4A @ @ A @ @ |? ? @@ @ @ ,A @ A P? X@ PA @ ? @ ? |@ @      @ @ H? T? ? ? ? 4? ? (A ? `A ? h@ L@ HA ? D@ LA x? $A @ A @ @ ? ,@ ? @ DA A <A     @ A T@ @ ? 8SV	 X         P      |f f g  df f g xf f Pg Df e pg  ~ g h     \f  Lg tf g g `f `g f g f 4h h Dg p~ g @4 f T h  g f f g     Tf g @g g 0g g f g f f g g g g f g g g  g f ~ Hf f f g f f g g @h h     } f f xg dg     N]                  lJ                ']               Vw\             L  \             8  ]             &     \                  ]             0     ]               v\               )x                7]             \             &     \             P 
                  ;o    \                 \                ]             
   i                \                   ]             8  ]                "\                \               \             z  \             F]               \                  \               4\               2]               \                ˽ X         P     / x \. |Y w |w Y  \ -  [ Y P [ Y     / ,/   v HZ - Z TZ Z  .  lY . . 4. [  Z   [ Y     |/ 8/ Z `  LZ tY t xZ [   4Z Z Y Y D.  Z  (v |. L > Z Y  [ 0Z < Z |\ Y ]     <[ v  [ $w dY |{  X         P    p	pN pO `N pL N |M M M O <L O L 4M L N L     @M N M M M M O XM (N M N N O 8N PN N M M O N DM N 4O 0M     N (M  N tM N L L pM L O N \N dM M  O M  M L @N O N M DK XL TN N PM O XN M (L N     O M M N 4K zV	             P   X         P   $   P     l H  X , 8 |        |      X L  $ L    p  0    H p            (  < P  d   x   h     t     T $    D       ~      G (             V                                  b                              v                               v               ,                  b                E                $x             j   F               c                                               $                n             F   {             |                  |               {             j|               {             @.   |             .   F   |             :  {               Vj                |             .    |             <      |             8<  {               {             B   >   o 
              ;o    |             l|             l   <  {             Н                            D   ,  n               8  _             vѝ             $                                ۝               j             x                h                l  S             2               0               C             
   U             <  )                    i             lP)                    \             Z             6   <   ם                                  v             |                               Ý             H   @                    h+I                             -J                                lq             @e             h   ȝ             @   N  vD                   }               `˝               l               (   ŝ               b                            
J                   P             8  o             @   j{                                               (     ĝ             X                 Ν               Z               p                  p   l                                pF             8                 P,                
             r             f  6             xtC                (   A             K             C                               `              B  %             N  pZ             ht             L     i             P<  !             6e                                b             K               n5             x                                 J                Ζ                            \               l                 <^                 i                             j   
(x                                i                    ז                               "             tf)                   ޖ               ܖ             Z               "      )             ,                  4                      y             x`                F  Ӗ                            8  `̖                `                             T               r  |             l  B               Ė             4S                             j             D  Y)                ږ             d   >                                           V                               ʖ                                            D  ˖                            J                  t                (                                               j                              &   &             6                          @                ^                             V               B               d                   h               7                            "N             Z   :   >                  i                                x                 $  EJ                             F   :ؖ             tI                {               b                   e             b  TC                f             ~    U                                                D                YI                             !             pdY               I             l  G             \l             t                  D  -)                                                                                 F>               x   ߄             
      jJ                   
             .   /             <  G)                               ;             `i                ؄                               j             ph                                                                 ٷ                            (   d    
            ;o                 :                ^   ķ                          &J                y                                              j   F)                             H  r   з                D                   ׵               )                             *.  j                                T                                                  x               *     ǵ             F               >  M)                                (                             
^             2                            *               :)                             J                  P                ɵ             p                                         ŵ                                       l             
  ӵ             v                                )                             v  ڵ               *`                 _             p      gu                  !`               F`             8  `             _                _               _                  _             PC                _               _               _             ^  +`               z                   `             X   _                 `                 Z  _             _             ,_             X    J                _             V  Y`             f  _             D`             _             u                ה             v             R! X         P         |  x $                   8  ` H  h  D     0   t   l ( 0        , $    |               h L    L    @              X X         P   
Ԗ  4 8 @  < ԗ  8      X     \  Ȗ   p $ ( L  ܗ И ؘ $  Ԙ ̗ x t  ė          x    T |  Ș D   T З     h ؖ   d ̖ 0  X ,           Ė P  \ Y	W X         P   h $ $ x$ |% $ $ \% p% <% $ # # % H% $ %     X% P $ # # % % % X$ % $$ 8% % P$ @$ # $ $ % $ # $ $ $     # <$ L% %  $ $ `$ # % $ # % # $ # (% $ H$ # % # $ d% $ % $ $ 0% $ % l$ $     T% % #  $ $ d ` X         P   Hc&	^ _ x_ ^ ^ ^ _ T^ d^ l^ 0_ _ ^ _ ] X^     ^ _ x^ ^ ^ _ ] ^ X_ ^ ] ^ ]  _ <_ 4_ _ ^ ^ P^ |_ _ _ D^     _ ^ _ ^ _ ] _ ] ^ (^ ^ _ _ _  _ ^ h^ `_ _ l_ _ d_ _ ] _ @^ D_ _ ^ ] \_ L_     ] ^ p_ L^ ^ <               w                               A                             
   J                x                R    X)                                J             n               n+             n*  r                 f                            )              w             N   >                   
            6  ;o    #             .0               dj                             v  t                          
+   I                             P`             d                               
  $kJ                R                               X   
            d   ;o                 l'                   =                               1             ^                 A                             ,"/             f   V               Z   JI                B                <             T   <                               x  `             F  z             "                     c               :             f               *  H                                            P  M_             P                   .             l               X                O             zH                L                            I             p                    N               4 
               ;o                   V             B                JD                   e             	B                    h                X-             D\-             H-               c-               R-             .   -             ~i                   f-                  -                -             V9                    -             ~   {-               V-                y-             I-             ^   H   -               <  F-             ^^q-               i                -             ^   @-                j                p-               ]-             .   r   i-             (  /j                O-             D  M-               -             HI             -             "   P   E-             "z  H                Z-               :   6-             Tj  d-             B   I                    -              (:-                }-               -                -               j-                 -                e-               -                  -             -             "   -               -             :     -             0  s-             f   -             A-             nz  -             N  C-               Bo-             d   <L-             V  )                z-             H     I                N-             0  ^-               W-               x]             i                   8             2R                 s             p  hj X         P    d	| H   c     $    | t ̅         Pd | 0 ̂ ld l \ h L Pc Ԅ c  <d   d   d X \       b dc   c t c b    P   H   d  ( @ T 4  D D P   ؃ H       c  c <  9                               "   1             j2               ,     
             T                  D  B               X             JC                /                            fHj                '                                            *   :W             :               >                $                 h             >  j)                a               Q             <  /D                   G             R    m 
            j  ;o                 \     b             0j             2             f     *                            t  aD                               FK             d   P   'I                N             0             tV             D  L             26                d                            >(             H    R             f  i               5               l,             6  `               L   L   RJ             ,                 h  -             6  ^             P             |   <                             >                               
֬               P%             t  .   	             &   t                  H                "                  h   \             `*g             fH                U               H             C                            N   B             P$             |  $                  j               @             d               lL   P             Z                     O             Z  )             pJ                   J               <                F             J             X   +             t,               l             LJ               V               *                                                V    J                             (                F   /                                                            &  .   +             DT               r&                                           &  `	             d               ^                  B                #                            2  0             >0                            t  p   J                               -                             `  H             `   a)                             (                                                                      L  f  jD                 *                V   J                               z  ~J                                h                               
h                                           L8                            ~ 
              J;o                                               $1                                %                	                   tI                                   F                                                 "   b   Xj                             ,   p             xxC                             2               z             pf               j  D                                           $  X             2               ,                 j   (                   ,                             h               `  $                $                                           X                                `  i                
                             L   B                r                 0                
ʷ                          D                            6  4                                               v)                               j                                g                   Ƿ                            B     3                *   Է               `               L(                   ߷             2  V               &>  5D             &                                            4  4                             ޷             
  I                                $                                   FI                                T                            :  r             
                    ,             $               |                :&  ŷ             @  :  ÷             N                    MI                                  ݷ             "             L             (:   ɷ             "  ܷ             z(                ͷ             :                                           b                b  η             >>               v                             F                   ۷             |                 @w                                            B4                              &               g                                 
                 ~                ^                0             B             ,t  S             *  Y             Df                   c                                tj               (                               ,  9                   x                m             x                  e               Q             .   `               ,             xR   k             `             X  H             j  {             h<               b.  O                +             |  e               *   A                             5             ,8.             N  `o                                              ~R  ْ             B   ~                1                t   N    
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8             |   t˞                            ~   ݞ               #               Þ             "   8             lN                               Ҟ               ՞             &  i                Ğ                  A                   Ӟ             8B                               p   Ԟ             :                                 x6               
                                &             B   !             8             p   J                             F   :                  ,   ڞ             f                            {J                ƞ                             ^                 Ξ             L             :  P֞                             p   V             `b  	             >                                I                +             X   (2j                             `  Fʞ               З X         P       H О  l p l L  @ H    , T  0     Ȟ  8   (   ؞  8 X T   ؟  ȟ     D L     ( d P ԟ    |  4 p         $    x ,  P ̞ @ T `       X 4 d <                  d     d                   X         P   ]	tO pM N O <P xN O O N M O \O M lN pN L     N O O N N (O TN <O P 4P (N P N |Q O M HO $N O P @O N Q PO     DO tM TO N O P M O hP N hO PN  O R Q O pO O DP  O O N  M O O dN M `O M O  N     N O $O O O                  d   d  '               '             X  '             B$  '                 f'                 '             Z   B   '                '               '                '             F'                '             V   |'             B   i             p'               t'               fNI                '             @'             d  :o'                w                    '               '             Z  "                 Ij                   '             H  \h'             J}'             
   X   '             '                '             ^  k'             :  8   I                   '             pUJ                s'             &  x'             P"  '             C                '               ^'             )             -      '                  '             <'               Tu'             D  '             &'               FJ                '               ~                '                  '             8  '               i                   '             2X  C                   '                '             n  '             '             (   '                '             a(                '               '             J  '             pw'               D                '               '                7I                '               '             xP   f'               $j                   '             X   8j             '               i'             j  "  '               '             &   '             .  '               V               ~             x  ~C                   v             6               R             X     J             Rh             Z                    6i             ,                              b   "  C                                &                    r                                           D   P   ^                K             L                  bF             >               v               @              R             f  ?             L  bf             T   R   Zw                             x    T)                                 &@  I             f             Rk             N                  &                                   C                F               FR   z             (ѕ             n                                P                   t   A               ~[                                           2(o                                         0             0   BYD                Y             j    H               (   t             b               E               )                             4J                   `                            2|                             4                d             ,             B   D                B  J             	                >             z                  PT               d]                                                    G             hm)                                ^`                              2                d  r  j 
            J         X         P   ?
  D \     4 (      |  L h        X P 8    8 l D , $   d    h ,          X       d     H T    x      4  `    x               y               T             R             Z    X         P            (    p   p   L     8     <    d   D  P    |     l P       4 @  (  T   \E    l     \  d    H     ` $       h      Y             D   N" 
                                    ƨ                                       4             ^               `  J  ɨ                                              \               
     (                Ѩ                *               jb               (  ި                               *                                             Ϩ             28               rw 
            <  ;o                 <                            $                  L             8                             ը                                           J                               2               
                "               &             h                              `  *   i                   è                                       p  Lx             $                  ̨             2  Ш                               J  Ǩ             6   *&               "8               5               =5               ,"5                T5               #5             6  v5              	  EI                   b5             f   J5               E5               i5             5             "u5               T   `5                             _5               5                (                5             <  w                   C5             Y5                  z5                  ;5               {5               Q5             &5             G5                  J                   K5                ^5             5             x5             
   TC                   55               @5             H  5                  W5               "             $      5                D5             6   ~5             	  S5             *  5             "  45             &(                   B5             F5             R  5                5             \  5             5                   k5                @5                  f5             `b	  )                 ,5             F  	5             \5             8  85 
            >         ,                             XPg                d                                i                ?               V[             $                 ~   J                   *             ;D                Q             l                   (              b   Z	                !             
  c)                 7             "                   x                <               H                `             h  $  0             T(                              R                 t0f             T  %                                )                          p0  "             ,   d   N             <  3             v                 f                   d             n(  M             FlX             &    
            ,H;o                 &               r             &                 ~{                 A                     -             ,                 v1                2                $9             &   ZI             J                     ]             6   "              V               S             n  .   
               '             l  m                ;             ^   F   &             f                 P                <   G               |                 ZI                                   l             ll.               H                            t                  :             h                6             4                j  v               D                Te                                             %  R               K             x                }                            Ty               H                d                               O             X   l             tG               C             >                  Vr   0             h   P             h  C               r             '             |Y             ~ hI             h             P   S             h  $               u             &  $                               >                Z                          f             `  *A                 :                
  q                               Q                               @  `                               (                   V             l  *                b             >  L               t                              P     a             :                N  {                            `D               4             P             ,  (             H  n              w             |T                l               "                  I                M               i                   /             >)             K               j	                &             T     <             h   @  @                              v                                                _                               "                                 0]               ^\             N   4  i             ?                             C                                                               
J                            D  ĵ                             Z               ,  iw                             f                    8D                             .               Xv                            ,  z             2               "A                                          "{                ,               z             
                          ϵ             &                x               4ȵ               '                b  T                 µ                            ,                 |                            (                                   R                           $               d  <                                      .  H                            i                                 y             (   յ             2                   }                W             ~                  Xd                          J                          v                             0   }             p  r                             \             $                               j  Χ             (   X               i                   ڧ             >   b  Mx                               (             .  ,             P     ݧ                            l  ~u             :     o                          b                                             A                ŧ             2   6  ߧ             N             է             \             ç             n                  R   D                J  B             H                                `   i             N  @               p§                           h                          *               V  s             |   T   !)                #                                    >p             D   X             n   ͧ             F   B   ǧ             `  x             4  ާ                             tY                             :     )                                            t                              vA X         P   `	- 0,  , , + T- + <- , , p+ H- x+ P- - T,     - + 4- , $- , + , , ,  + <, , + |- , 0- X- , t, + - ,     , + 4, p, (, d+ + l+ + - + , , , d- `, - |, D, ,, - @- l,  , + |+ , + + d, h+ h,     - , + , ,                 (j               .                                  8   A                                             R  ˳             >  ׳             z                ,             j                                  ~                =J                -             "                   X               @   '                8                n               Rճ                                          2  6  H               ,                
  ϳ               4             P  yi                   +               س                            HL1             (  x             
"D                ӳ                ĳ                               2  V   
                              P   ޳                3             6               R   E               ͳ               9               <             \                F             R  /             T   L                ,                  ۳             N$                     *                          &  >&j                
   $                          *                                             v                  G             .   Y{                X         P   $ 0@ ? DA A @ 8@ @ P@ @@ A @ lA p@ @ ? @     @ l@ $A h@ ? x@ A @ L@ @ $@ \@ @ @  A @ ? A @ XA @ @ |A |@     A ? > @ d@ <A ? @ ? A A ? H@ @ xA D@ 4A @ @ @A A `A  @ A ? @ ? @ T@ \A ? t@     A A @ A @ Xa	{ X         P   pa	   t        x     8     t   0  |  p   | , $ P  < L h    `  L       X     8     t D ,       X `  h  4 d  D   <       P      ڰ             
   !~ X         P   $  0          4  h  p$      `    t   D    h l     D   T    ,          p    d        , \  x  L              <     @     S X         P   h  ) ) ( ( p* ) & ) ,* G ,) ) ( ) )     p) ) x) ht P& ( t xt ( (  * * ) 8) ( & ) ( |) * ( ( & dt     ' * ) (  *  ) ) ( X) ' ' h) ) ) ) 0) ) ) (  ' H) ) ) ) 4* (  ' ' ) (  ) @*     ' P* ( ' )  #             n  
  ,                K             "   N                               &  i               @             pL                                              <I             dw             $|   >                            zB             P+             h  p8                          j   R             f*             J  ,   )             T   T               <   N  1                   .             8   :               M             r   1                 m               hH             @   g                D  3                  &             v               @               FJ                   
             (  v   ڹ             &   V                  A                   +             D  ۹               NA                                &  ,             &!             T   i                                &                8                                 ݹ                                	             X   :                    .             "             n  l                               ع               й             ,  @  (             ɹ               ~                ҹ                             
  ,                  p_I                               zȹ                            .   *             B               L  
            `|  ;o                              $                            T                            l                .  x             .                <6                j  ʹ             F.  ٹ             <               b               ~                             F                     H                ܹ             :  ,  ߹                          \                              z     ǹ                 
                             $  6                                 ݫ               T                                   .ZH             |	                               (                >               ~E               >I                
             .                              0             
   Z=j                    $                                  S                  ,x                D                !             `                 pF             
                  R             J             s               ]             T   D   `             d  j                H                `   \                J                j             x  fr               =               |                             R  7             dJ?             4R                  O             V     u               w                   C             @ >                                              6             z    z                R  J             "                -                            0  b               k                   c             Rz  =             0  \             /               j                r             |                2             T             P   4                               P               3             n6             "  A                X                 ?             U                  l             )                                 ,  o                               (             X   k                            j,  p               <{                                 _               f(                             ^j             l               X   q             l                                B                  F             $  V             bn                "               l   h  u                   ]                             @               b0             h               4  f             X  /             O                !                              9             t  ,                b               J                                 <                             P                            l             d  "J                              T    H             B  2             .             *@                R  %             RP  ,                0             	               "                T             xH                R                               
   F             
*                                              b               B   Z               R             
   $                             -             F                  b6                R                                  n  Z               x                                              "   3                   '             r  J   8                                +                                   D                 )             ~	             X   n                             d                  4      K               L             \                               8               ~                               2                               j                  J               $   d             vd             *d             >  !d                C             H   B 
            @                                    d                  v             6               \                p               x                  <T                  C                                            J   <   >                               ,               <   5                                           T                            I                              '                 r 
            
~;o    	                J                                0D                             f                 i                             p  |                                |                 $             ~                    *I                                :  1)                             
                :                            j               `2!                                                           b  .                  .             2J9               v$                 *                                               Z  ^                               
                H   X             T   j                                            TL  6                 r             "  (             P   J                                             t               P   i                1                          X  YJ                                            0  3             z  )                    ?                                                         @  |             \               :               2                B\|(                -                            R  n               C                                     v               <                  B                8             ^               2   F5             >   p  x             R   N                d  dH                L             .^|                          n  (                   I             N             ^$             :     I                                                         *  }                          (                 h  "   +                            V8f             J                  V  4                   A             l                  m                X  k                            S                
               *q             >                *   i             l             2   @             Ln               2             "    .             |             *   X                                 [             .v3             ^                  8               nJ                _             p4             B   F2               )                                Z                 N  0             &   r  U             X   h                 `w             hh                :             ^               p             &               4                                            H                               g(                                               2                              "             "                   D  (                             |  ")                                >  #	             b             Z                                                         `   
                  >I                             H                              v      
              ;o                    J                             t                 ,                8                           ,             :  T               z                              j             m                            l               <                                                                   H               b                                                 `                &                              x  *j                                                	)                               D   J                          ht                                                &               
                             H                F                B                             @                                                             b  l                            V             *               b               ,                                               K                |                    6             v                            (                               L     i                    2                                            |                 J                                Ro               H               D                              f  4b             j                              z                            ZJ                            0&  k                ]J                             $             X                
                j   m             B     I                Z               g 
              *;o                   H                s             0   I                 F                          E                               0                *  :H                7             ~b  l(                Q             Dh                B  W             2   I             \  (             R6               j    eI                             l   ^             w             *   H                           a                x               (                                   <                  C                \             vS)                ;               
               
    |               2j                                v     I                                P               X   d  L             D  O             p             l   d                              (   C             vde             P  ?               NCj                    S             Z  8l                H             rH                                  i                	                                               b                            n  Z              Lw                                            l                                                    d   '             $                h`                H                     ' 
            P  ;o                                                  bx                v              V              J"y                                     n              ,     /%                                 j              *                6w                                                                   N   T                 >b                :   2                 m              X   4x)                              V     p                            \              \                                   X    r              F:                                 "                <                      ^                                b              0                w                                o                 ,                   x              6                              z    |              Z                $                                  ~              \   8                  *                               <              ^                Z   \                                 *                 r                  $                 0                                    FlC               TC             2      C               C             T  C             C             B  C             (h  C             ~2             C                C             *  td             2   C             N   w                    C               zC                  C             qC             (   v   jC               C             2  C               j                  C                $]C             4  @x                   nC             `:  C             (  T  C               C             fr  h>             J>               -             VZ  ">             Hx  FD                    !>             "   z  >                   >                 ]>             =                K>                  B                C>             |     J>               7>                b>               >               N9>               H>             B6   '>             
  |=             ^J                >                 =                                 N>                6>             J   1             "  P X         P   H  @ H   0  l   (A p  |@ @ ?        A  @?  @    A  @  A @   ,A  P  @      A @ |    $A  A     0  H @  A  x @ < d@ @  @ 8  @ @   X     A   t  ܘ                             j(                   +                b                8             8   E             ^   _             "               L  H                             K             R   6                L             :                     b                ?             00Y               @R             	   	   Z                  V             @f               r  rI                   y             ~                  D  (             
  <D                t             ^z D                             X  r             H  Bz             b               > 
            n  ;o                 l  s(                3                m             t    i             p             B               
  ~                 u             4j                vP             T
                                   ~7               -               D   T               s             04D                                Z  F             @4  n               R               (                 4               Q             6  vS                U             v  e                                              n/             X  D             j                .                      >                             H                                           H               J             	     d             
  0             *k             $               .  tG             &             *  9                               bX               :               C               h             F   U                \             2               @9                |             $   p   ;                               ~   h                V6                                 D                                Z                D                 C             :               D     :               #             *               `               0   '             
               n  v               (                p                                ^                                                  F                          p   6                            (V                               d   x  >             t               8                             X  =                            ?               2                                  F0                                           Z   l   2             H               *                  8p                             x                                              8             r               @             :               ~               6             h                  8H                                                	                           B   )             &             $  2             I             	               ~                                F
               8                                           <               hy             zD  `             `               "               Z               \                             X  V             H  T  D             r   J                g               S                j  (                   R             W     u             T             HƯ               >             X  N             NB             n               r  ,   i                   e             &#             6I                0             $             I                 q             T   d  J                   v               Di             *I                @                                
            b   ;o    H             H  .             &      G             h  \;             	                    A                            C                            	  9             ,             l   D  H                                             (                L                J                	                                                                   @I                	   O             :             x                  x  k               
             	  *                L  M             2   _                                            Gj                b             x`h             l   ~               
  =             @   !                            z    7             N   l             "C             	      a                |             >   6             P               .  4                  	  z                             
               >                   S"             $  )"             <	  "               v   "             RRp"               9"             ,  Z'"             z~H                   }"             2  "                $"             ~  J"             >"             0   <)                   "             J(   "               GJ                5"             F  "             P  *D                   "                  "             	  &"             4  Y"             ^  r"             V  i                "               DI                   X"             #"             |   D"                X   "             $  $"               "             R    v"             X   ."                 "                !               "               &   +"             r  \"             t  "             P  H                   U"             "               !               <  "             x   \   <"             D                6"             t   @"               "             
"             0   J                (   I"             6  oI                 "             v   a"             <  )                "               "             IJ                   %"               ^R"             |R  "             *       X         P      k k l Hk l k Tk Tl (k j k \l |k l k k      k $l l j $m <l k 8k l Ll k <k l `k  m l k Xk m @k Xl pl l 4l     tk l l k l  k dl l k l k k $k k k m  tl k k l l ,k Dl 8l ,l Pk 0l l k k pk     k k l Dk k                    =                                                                           ^   {             L   D                @  k             v    $                 X         P        4    4 T < d 0    L  p      D (4     @ X	  x x  4  l  h 3 $    T |     |   3  ` F    (    D4 H         $4 $ 8 $ p  l X         @                   x                  (             x
               J                            4  J                    o             L  N1                &             8      4             L   I             ~                ;             pw             D               >:D                          bp             x   C             m             Dn               \  i             4   O             2b                                    ^  f               t/             
  #             <  ,                2             6             |  {             n	                    H   C                =               KD                ^                                 [             .\  $                A             
  n             A                    Z                            fJ                               <                %             V     K               v             *               (      <               [                )   8               )             :               @@,             R                AD                (                                           $&  A                                                \  D                    -             L;               2   '                              -               *   O               R               4             (   w                             &   Ð               r                             :  w                3                              n             Bː                 
  ِ               א                  +             *             R   x               <               
   &                ,             F             @   .             w                 $                Ґ                               &                (                t                   f             (
  x                             4Tʐ               x                 <                            f             4                     L               b֐                            4   ΐ               q             
  *             &L                   !                2                                 (ɐ               P               (	               .
                                   ^             :                  (                                &                f             
                8                               (             8N               8  t             ~   
  7             0=             p
  j                 r               Ti                             j   N  L                t                 >Z             tf	j                             h   s                          
  HM               a             ,   X             .J               HH                             r
               8     R             f   \   C                          4               I                               |             R  I                
                J                  lI                             g             
.  m                            j                  F                  GI                                 2             ^               0                
  8H                                          ^lI                                 O               u             V	  ;             &  o             Z  P             @c             D~             z   I                                 v                  p             2             f                  8H                          f  Z                              2                l                          &  ?                   I                             4R  }             l   WI                E               N                 w               AI                T             LV   v                t                f   e             N  {                p                 @j                   @             j    h                 6   I                   K             	  Wj                >               \               l             &     J             6  I                             a             d  .                 F  k             r  .             fP  2               6o                  z                 &                               vE             b  ,               h             r      >                H[               i                             F                                 A                0                \             P             H   y                 ;             |c             ,x                    B             ,  L   #             $  w                X8                            D  u                n             $  |             @(             	  H             C               $\                   j             4X                m             l             `L                g             fl~                9             L     q             X"                             ӆ             ,
                               :   J                4               d               :l  ]               t                z  1                            R  i                             b  @             tB  _D                   D             ?             h  s                                )                  v                          \	  !               LA                `               v             @V             P
               	  p   K                7                              T             &                   ti                 H               =               <=               =             T=             (                s=             Z  H=             q=             C=             	  =             &  =                  =             0R=                 i                ]=                  w                =               =                *=               <                =               ?=                 x=               #=             R  =                   O=             |<ND                   V=               <               f=               B   y=                z=                p=               ==             	  Aj                   c=               W=             t      2=             0  G=             |	=             z  3=                   J             Z=                2  A                   l=                =             *<               xA             t  (                mA             :   `A             &A             f   P   >A             (Jj                   A             <A             N  $A             *   vA               8   SA                %A                =A               'A             n  pA             i                cA                  A             ^  AA             `   EA                A             H  Y                A                _A             D  <UA             2  A               \A             29A             "    fA               @  A                
A             ^   A                Z   IA               RA             J  3A             &T   3#             N  #             >H  I                #             V1#               (                p#                            F
               b   <  /             ,               @                 `                             0h                               d                 V                   r                 *<  7/             `   *J                </               /               >  /             PS/                $   A/               t/               (/               R/             B  d/             z  /             V  ,J                /             b`k/             @  dI                   -/             22   r/             ,H/             N   0  C/             D/             L  W/               )                .             */             
  /               j                    `/             f  ./                |/             b   Z   (                
/                  0/               V/                n   /             y/             (  &/             .U/             @     H- 
               ;o    f/               4   $             &c/             h   #/             2  e/                {/             "   */             Z     +/               K                G/             R.             P/                   /             :%/               
   }                   /             u/                [J             B/                 /             6   "             1   /             	/             ~    ]/             	  HC             /             /             V   `  q/               ,  K/               F4/             :  /             )/                  2             2d'               &   3 
               ;o    > X         P   O	' ' & ' & & <( & ( t( ' h& |' ' T& &     x' <' & 0' & ,( l' & ( ' ' ' ( & ( D' ' P( `& X' ' p( $' 8'     ' \( \' ( ( ' L( & L' ' & (' $( \& ' `' ( x& d' |& ' & & l( ' & ' & & & 4( '     |( & t& & ' <               F                   l               \                                           ~                             l                    4                                                  Cx                                 b                                	               f               v               z             d                            J                
                            j                                               x(                                          j             X                4                .                  H                                  N                          z                 X                            J                                                   (                               r                vp                @                                                               
                             F  I                                                 2               V               N     C                             Di                                            <                                      |              <   i                                  ;               ;              L  m;             &   -;             V   B   z;               ;                ;             T   I                    ;               .   A                F;             &  '                };             d  l)                t;             ,   %;                 i                ;               I                p;               "1                ;             t   N;               R  ;                 x                l;             ,   ;                ZA                   O;             h  4e;               T  r;             P   ;             :N  i                   I;               d;                R;               k;             JD  $;             l;                ;               ;               X;             Di             ;             \<;                ;             h  !;             B  HS;                                  P;               G;                ~`;               v;                6;             j;                hM;               K;             J;                H                   [;               ;             pT;             :Z;                 `2;                                           F                 ;             *               `   (               $               /               \:               \)                             $  v   ]                             &   P             n  X             ^                Z             -             l4  I                    T             2  |             x   j             Z                            B  Xx                                z$             F   C             (   i                	             D  `                Fw                                *                 N   8   D             PC                Q             (  |   %               *                            O                            v  f                            L                     M             tH                &             .                     x                =                            q(                   #                 '                            *   8             T   6                 (                R             |   lU             .  >   I             (  +                                             @  `I                                  b             >               N               f                               "@                          BF             t  [                PH                               3, X         P   $ ( d  H  (        4 T         D  X L  P ,    0   D |    d    x     h  L     ` h   <    $ @     < 8     x H   T t       8 p                                                                                         P               J  Z                 9c                ;c             d  ~c                ]c             )c                <  {c               Rc             F  Xic             \  	D                   b               ~  (                c             
  Pc             Jc               c             ac             b             ,      c             	  Zsc               Yc             l    Wc             4c             :	  \c                 *c 
              p        c              X         P         к   Ȼ  t < 4    Ի       | L     l X    P X  <  л  `      H T $       ̺ ػ  8   h  T     0  d    `  Ⱥ غ     \ L d       H 4 Ժ                  V                 |  C              8n                "             
                D              I                             j                                    4                                   \h               N                *   XI                                 K              j                                j   T                            r|                  /                
   )                                          H                 "              t                             V  
                x                $                  *              H  \)                (                 
   |  f                                Jv                4                j                >                ?              4   n             
                                h$              $   H  .              "                                  t                    >                                              rA                             V  &                              D                   $                                                &D                                                                  # 
            T   ;o                  6  .D                                   ;              J              x                                                  V  "              R  B               )                               :              j~  #              B                  *                r               (   h               h   L  N                g                                 M              4                   ř             <  0                .  D                             h                <  )                    ֙             N                            `   `                J                 S                   )                 X                P             .     r                yI                                   H                             P  _             ^  (                                    |             2  \             .   ~  i                ~                D  I                   a             z             t      G             L                                                H                                                 Z                                f             "                ti                                   A                                   י                2  ę             B               B                                  ҙ             2               $                 p@               \                  )                Ι               ə                                                           Z                                 l             H  x             :  v             V                              @                 o                          8  I                             .             :                                                                              :   }               bI             Z             t             nc               ԙ             @  
   >j                4                             
                .  F                               P    @             >   h             # X         P      | d p , X D t t    d  P        4   @     ( <  |    x h   8  ` T             ( T  h 0    X   T p   L 0  T# @     h        L  8     R X         P      7 8 L8 7 7 7 7 7 l8 @8 7 7 8 7 8 8     8 d7 l7 <8 8 7 8 h8 $7 6 7 47 <7 6 D8 7 7 8 9 48 6 p7 6 07     8 7 8 7 8 8 6 ,8 7 7 \7 `7 7 8 (8 7 9 8 8 87 ,7 8 \8  8 8 7 P7 8  9 7 8 6     7 7 08 7 8    X=             % X         P       4 `3  4 3 04 3 3 ,3 3 3 L3 4 2 3 2 P3     p4 4 <4 3 3 2   2 4 2 83 4 (4 3 |4 3 2 4 2 @3 2 4 3 4     2 2 3  3 3 3 P4 T4 \3 4 2  4 2 t3 4 4 3 2 3 T3 43 3 3 2 3 (3 3 3 4 2 4 $3     3 4 2 L4 44 xp	                              |                                ||             V                "                               <   p             |                >  b               <                               h:                                              h                                                             	             T   F                D                                                            h               f             8@               "             ^                  \                                z              
            J   v;o                 L                   .             $                "               f                                C                                   CD                                                tZ                                              N  X               :/I                                                                   P               @(                                             <               v             d             D               v               (  .                x                B                  n                H               f  l                                               
             <N                                0               I                                   I                                @   #             0               ,  O)                B   ݲ                 0             ,                 +               4               XJ                             (               P  @             V                N             n             0                  j4                                C               R?w                    ~                                                  ?                  '                  F             $MZ             6                  D                   f                          r                 c                              l             h                D               z               |N   y                             h   j                P             T~                                     l                t             u                (                             :  )                   z             8  j             P   Br                            |  4                  o             ,                V                  W                             x`                                                      |   #D                             V  i                            <                              (   g             pj             4                   ~e               	J                                             
f               X  O                 L   H                X             
   ~                                                                                                    N  h             j               T                 H                :                            :                (             X                D  ^R               |               Q 
            6F                         N              \                j   !s             2   ~   1s                  r               H                $s                B#s               r             <     r                /s             p   r                P   	s             
s                          /      r             NNs             ^  r             `|s             X	  r             .  r 
                    s             F                  f             v    X             Tl             
   5)             |             f               <               Dh             \                  I                }             j  [                H  j             8                 L   X               f                x   ~  C                   r               H                 N                                C                L                  S             &   x                R  ]                            F  T             8   &             \   D                  c                            =             4  GD                                             f  `                 Z                          ,                f  $   8             0   Y             n   i                                              <Q             .  rp             (                g             fN  z)                             lc                               C               X                                             R             BJ                   b             P  U               n             \   z             ~  ^                              E                4                            j                          NC                             R   v                                 N             v                 o                G                    T                          L               2a                             R   .I                                            T   F                 
                                   6<             |Z   c             
   N   P               y                (:             v   u                                         z>                            g                bG               )                              +             d                @q               Z               X             r    K               f                            LLJ             ^   _)                             t                .t               b  
                
              
                  N   @             ^  =             &   I                   p             F             L   l             i             @  V  E             5               S                \                             :M                 pXJ                   O             V               .             d    t             L  4               gD                ~                A                          Z   r              &  d               I             &   ,               XD                A                   tn             r  nI                             P@               2   w             4   V                    0             h4  w             d  %             V                            R   :   /             :                  7               }                "|                             B   j	                 ^                          R  0   9               ]               S             x  A             NbD                            F                      Y                                   5                j  1             P               j<k                            8V             o                               {             2   >             BG                              v3                            
               6  .                   S               V                               6   P             @  v4             X  X             $  n             l               ]                                         Z                               V                    g                             pb                  6w                 m                             H  e             $                     i             cI                             %             2  6             :i                                 0                                                            ^               a             *L  A                T                @             N  F             .               B             $  v  (                	   \             lc               j             
     s               +                h  I                v             z  (                   }                            .             xJ                x                                                   f               J)             4   M                u-             K               @y             P  J                             v             >,             H               ~ .               B                                             ||                                ^             zr  )             ~                  Z             ~                                               Bx             n   `  6                   A                r             F  *   1             A                             )             `  Lj                                            8               D   \                 :J                             Z             r,                                                     6                               *  |             v                              |             V                Z                R     	             ||                    ,             h   z(                               Z                               B                                                ~
  5                                                      F             d  J                          |                             J                .                                            
  J               P                                   (                             <   i                   *             p                b  
                 
                                              .                 >   4               :p                   ,  H                                                                           p             H               N
  7 X         P   ;    4     Լ D   0 | 0  t       4 (  Ľ x , н d  t   l p  l  8  X Ь             \ T  4  4  p  $ Ȭ  @ | <   L \   T    ( ` ج         $     Z             jvZ             x  fZ                   Z             :Z             H                   Z                  Z             D   Z               :   {Z             8vZ             VZ             
=)                Z               I                   Z                Z               hZ             Z             v  Z             Z             r  Z                  mZ             F  iZ             J   
B                Z             4	  Z               D  qI                 
   Z               F  gZ             fI                Z               (                 Z             &  Z             R   `   }Z             J   <  Z             V   8aZ               PZ               JZ                  Z             \  |Z                Z                n   Z             4<                J=                m=             R                      {=               %=             ~  e=                   k=             x	  x<             	                  o=             b  -=             )                n=             <                  Q=             <   6=               >=               DI             F=             :D             <                <                <             &   )                0=             X  K=             p  d   g=                 d=             n  z  ^=             I                b=                Y=                t=             a                   1=             
   >  8=                +=             '=             <             l             <             N=             f  =               B   X         P   25	 ~ 4~ D ~  ,~ ~ ~  ~ } ~ ~  ~         ~ ~ ~   ( hi } ` t ~ } ~ ~ x ~ L (~ ~ }      } X 0 |~  ~ }  } ~  ~ ~ T~ ~ }  ~ ~ 8 l  ~ ~ ~ H~   D~   }       } L~  ~ <                 V                ,              ,                                                 u             z  dJ                              Xb  U             \                  N                  w             6             (    J                9             0X  O             2X!             F               e             R,f             t  =                1             V  f@               6               H                    rr                T             \   
            H;o    Q               F               [             2I                 X                  8             4   D                            f  Z             T&             d               TP)               -               ^i             6e                C                             t<                            v   H  C                /                 8   p             $    P             j2               J                4                             v               < b             2   `  ?                 ]             d'             z     M               G             r     )                K             2             6  H             2>             >   :             |   z                  (             @   T   #                                D   b  B             j  bW                             7             P   F             \   J                |             F  %               D             zD                	                                 c             ^i              T              N(  1                  |                   M              ~  .              p  "                    ^  x             "   j                f                                 b  _                5                                 l  `              (                             &   B  n              \  *                                 d~              2                 x                              h                
   T              Z  Tx                =                              X                "  y             *   G              0   p             ^  
                 f                            ~                  .   w               {              &   p                              J                                          ҭ             X   zϭ             ,   *                                 T                 M                              )                Q                            d$                f  ?              J                    b                                 \              (  e                               r     h                   :              l                  zH                 J                b                  8                                            ~   3                 x(                              0  dz                                                                    f     (                 w              b                b                \  b               b                                                             Y                                           .trD                   H               R                                                                             :             .w(                                             J6                B               p%                          t  2             4                 (  ,             >                 
  K             ^     (                             dP                                            V             7                              &J               +                          &                                     h9             ,                 M             :                                              n               D               
   2             T                   t$4                                           J  6   G             
             *             "  D                Bt               T               $     X             P  l             >     ?                               /             |  v'             x   p'             d'             j  '             V?)                '             ,   '               L'                  O             f                ,               f   dE               t             V                            V  Z             <  
                      ;               W                  w                                :B                             p                                R             :Q             x                            \                          H               2                 3               R                  ,                                                  X                <   ?             B                  8                                                                pG             @  [                            h             T  .                 -             V4             \B  I             P  6             6                                     
             T             =             <   X               !                @                  ,  !                             2                 $                            1             &                T                                O                          b                                 x             4  >             hx  7               K                R  x                             L               ^  "                 /             n               
                 dI                  Ч               ^             h(                _             >  ^             Z   ^                 _                                   ^                  ^             L   ^             z  ^             b*_               6^             _                  {^                ^                X^             l  _x                   ^               V  ^             ^             
  ^                  ^                 ,  $_             j  ^               5_                ^             ,    ^               ^               ^             $     ^             >#_             <   _               $   ^             2   _             8     ^                !_                ^             X,^                ^               _             &     _             |   ^                
'_             ^             R  ^             D   &  ^             *   ^               ^                                ^             ^             _             
   _                _             ,  ^             (  ^             V  ^             z                  ^             "   ^                 ^                
 _             X   ^               !   ^               &^               n/             .     Q/               Z/             "     /             d   L   :/             (  /                ~/             0  [/             _/               z/             
T/                8/             Z   B  /x                /             p,a/             LR/             2/             ~                      R                
            .   ;o                    w                             5               :   L)             !   :5             .c5             $   o5                A5             "<5             v  }5             4  r5             p    l5               8  5             5             
   
15                O5             F_w                )5             l  I5               (                  /5               5             "   05             5             Lv9-                I                -             v  a-             PT   [-             PL-               -             ,?-             $  V-                              -             t  -                                Y-             *  (K-             
  B-               >  7-             zf  n-               -               J                -             44  74               f  X         P      \f f g f f h @g 	 g pf Tg f $g g 	 f      g f `f `g g g g g f g $h g g hf Dh f h e f lg g  h h hg     h tf Pf |g xg g f Xh f h f Pg 8g f g f (h f \h g f g lh xf ph f e Lh pg g h Th     tg th f xh  g                 	  )                p                                ʔ                 ٔ             J  ~               i                               ܔ             B             n   q                             b               ~8   m                 K                                   8             &  ^               f               y                              F     ڔ             N   n             *                                 ǔ               Ô                                         @                 <Ŕ             <             D  B   Ȕ             b   N   }             6                              Vp   z             f                                s             n   ϔ             @               (  D                  v                H                                               "  k                              Д             @   i                            Ɣ             r  N   n               Ӕ                ,             6B                               l8                              T	               (                          xl             H                                   I                   Ĕ                                               *                    ֔             H$               l  (                4   ؔ                 
            Z&  ;o                 p                 u                b                (  `                            (  ۔                                         tޔ             "   T߲             V                                             :                                            6     x                ޲             
   8B             x                                   F             2                &               #                t  (             	                                (  4             n               .               I               J             ^                   .)                               :                  .۲                             T     A             rx                  L                ܲ             dN                                      j               ز               E             H               2  :             8   PJ                               ;               *   =             $   ²                            $     ɲ                                             
     Բ               p                  ò             *                  Ų                                        4  e             h  f                                               Z   ;             `                   ~;               8  5;               ;               0I                ];               W;             TT  q;             ^   r;             pX   Q;             4B;             &3;               ;             ft  ;             |n  x;             j;               P   =;             j?;               0;             vyD                L;                H   +;                  9;                0(                	   :;               #;                L;                  );             8  V             V             U                U             z  V               U             $  w                
   U             ^   H                   V               J                    U               .   U             T     U             bU             6z  U               V               U             8VU             >U               U             @X  U             U             ^TU             l  PU             8BU             b  U             HC                   U               U             4F  U             n  U             r:U                  U               x                U             \  U             .L                V                  U               U                b  U              T  H X         P   ?
   ̪       ` 0  8  ة      l 4 h <    H     L  $  t      ԩ p        (  ܩ x   Ԫ      d   ,    x  | T Ȫ    | Ъ           , 0                 Z               :                   V                                $   n                O               "O               B             |  B                  B             4	   C             `   \   B               C              H   C               B                   C             6  DB             ,,C             `B             
C               L  &C             ^   ~  (                   C                 B                  B                C               &J                B                B             l  ^I                   B             R     B             C             b   B             R   R   B                n   C                   !C             
5C             ~  -C             l_             x    0_             D  t  Q_             .  _             8K_             p  r   c_               0   i_               P_             
H_             @Y^             Z  *_                M_             v  F             (                2s             
   O               W                                 w                             r,               HK                                V                               \                  Z                                                                   K               8               F                    
             ";o    A                          h                                                (I             6     G                                                              J                T             $@                  J             t                S             R                                             Zq)                                                &  ?               @                8             vr                  Q                Y               b             :               )                                  2               XX               t               /                                F               B   x                
                  E             x
  *                                             R             ~             7             J                                 `0             ,                                                <  +               C             N                  	   M                          P  $             ,   D  K                  K             L                L             K               !L             $   *K               0  K                L             K             4  K               L             (L             3L             (     &L             N     LI                	L             LL             *  K             X  ~K                )L             \  K             @K             \                      K             X   J  I                K               H                    K             *L                2   B             X  K             ,4	  !D                K             R  K                K             K               J                             J             r  K 
                        p X         P      D h t  $   4     @        8       < (  `   x \                P           P ,  ` |      ( l     $  H      d L @     I X         P       T@ l@ @ @ > ? ? > ? ? p? @ ? > ? L?     > D? ? ? @  @ ? d?  ? ? @  ? > h@ ? @ > ? 4@ @ > > @ ,?     h? (@ ? \@ ? ? ? ? t? ? @@ H? @ @ > > @ L@ <? X? x@ > X@ ? > ? (? > @ P? ? $     ? P@ @ ? @ P ~              hy              (                 8                   J\              @   Ɲ                   s                          "                                                   t+s                   h                                As                   i              j  Ys                   ]              N  {s                   S              8  |              
                    Ws                                l                 Ts                              "     &                 q                                                2                     [              dq                              P                2Es                                                                jVs                ߝ             &                       >s                   O                .              D     s                                   8  }                 ɝ             0Y              6                 >  e              8Ns                                 N_                                  bPs                             0                                               |   Cs                v              T                ^                 g              ZIs                                  <                 F    <s                                   E                                 
   J                              b                  	  a              X     1s                                                 ,*  ~              ,                   D                .  
                @Os                                 =s                              0                   %              6  C               x                C             \C               C             `  C             fC               :  C               C               XC             4  C                *x                C             S  C                ,C             <                      C             F                  uC               C             C             C             :z  C             DC             6   tC             p|   C             R   C             "   C               C               C               xC                v   C             C             ~C             :C             
     pC               mC             J                  C                  ZC               tC               C                 ^C             iC             0  C               C             t  C             .s                C               C                2jx                C             bZ  fC             T   C             @  C             zR  C             &  |_C             C             <  C             F  F   $               t$             xN   x$             
  Z$             h
  v!                $                 &V$               `$               &$               
  $               $             $               $             F$                $             t  $             j$                (                Q$             .  $                "f$             "      $             $               (             $               D(                $               $                  $             "
  o$              )                   S$               )                $             2   [$               w$             $  $             	  d   $             `  I)                $               I$             .  $             
  $                 $                  y$             >   $             j  (                $             z  ^$             0`                $             $             8  $               (                *   $             z  (                   N$             f   $                Jb$             6  $               $             H  $             `2                x               l                                                               P             H             j               "               R               R                              >               V             r                 p                n                                                           "                t                               F2               j  <             `                             v                             
  6                                           V                  @                                              :                t               	                                 n  $             2               
                  J                             
               \                                                               D                \
                 @                          n  v                              66                                             T             j
               N             &               0             P\               V                                         z   `                .                   @               *             bp             8   '                            {                  ˓                             p                
                   .             .   }                 $             X  \               "             @  C                h             X               .8                  "ғ                            pד               ̓             ~B                                    3                 N             t
  Փ                                                @Z             B               @,                            @~                                           <                N  >               $             X             |  ԓ             p   T                               b               
  Rm                              ^ߓ               %                62               ؓ             R                 -             d:                  
             X  b             
  ѓ             @~                  i                             <                    T                f   m             N͓             @               v                ʒ             H:             N             f  +                               z                "
  ړ             	  p                |U             "      U             t0U             U               <  J                U             U                ex                N   4@             ,U                U             N   U             ::   V             0U                 U             PU                  U                  U             .   V                U             :,  U               U             4  U                	V               U             ,   /)                U                  U             n   U               V               U               V             d  U             z    U                  (             U                U              `U             U               \  i                U             4   zJ                   U             d     U             L     U             j                 H             t                               6               @                   Y             ,                L                                                                                            4                  6	               F                                  z                              .                 H                  `             8P                p             	                 Jx 
            
;o                 Z               *   "                               H   	               *   2                            z                    R[                *~             8`             r    u             D6                                                  w               m               W                                             4   s             d                  X  b                            x               nv             (                P               	               \                               Z               h             ,   L             L   V  u             b                               (                ><                r                                                                              4                	                 Z             V   j  tZ                 {)                   Z             jZ                Z             Z             >   C                Z             ,Z               Z             ~                Z               Z               Z             Z  Z               J                Z             \Z               r)                9   Z               Z             \  Z               f  Z             (     Z             	  Z             vZ                .   Z               C                   Z             h   Z               >J                jZ             `     Z             H   xZ             p   X   nZ             	  Z               Z             zv)                0   Z             6   $Z                   eZ                  i                Z             Z             Z             sZ             d     Z             ;               ;               r;                   ;               xI                   ;             @B(                 +               f;                ;             :J  ;             2D)                ;               ;             p     ;               >   j                   +             ,             ()                   +             R^,               8  ;               N)                7;                  Y/             N+               :;                  ;             |    &w             	   ;             T     i             	   ;             z   I                ;               I             $   ;               T  ,                ;             "   ;             (=,               ;             \   ;             `  (                +             $  ;             $H;             t  ,               ,             JN;             h   <             
,             |     ,             r  +                ;             J  ,              <   2                  q X         P   }	     | @        8 d H      h       \  ,      T  Ps  $ 0  ( `          l   L      T 0 P   $ x  <      l X         h         d               ~d                 d                 i                    d             i                d             46
  id             6                   *             Hx  !                
                      Q< X         P   t	ܸ l X  Ը ع   D 0  Ĺ   P       x T  ĸ  ظ h  L  t   Թ | 8   `            | D H l l ̷     p   ȹ  <   d   t l P й  t    d  (     4 \    x~	 X         P   8~	k Tk `k j Hk lk lj k i j j @k j j j i     k  k i j k 4j j j k Xk j k j i <j xj j j k j Hj j i pj     j 0k Pk hk k j xk j k k j dk tj @ k k  j k k i Pj i k 8k j k \k k k 4k k |k     k k j j j F             b  4_             8                 X               rl                T               F                ^|             d1             TR             0x               5             
     I                              z             $ Q                            n   b                              L                               V             Hk                  @)                A               z             	                   U             h              n               hV(                                               <  !             	  +             "  X  @               L             f   D  v               4             B 	  w                3             8  6   q                W                 O             x  ,                e                               D                  4#             {             r   a             $  fG             (                   p             ^             T  zY             n                      D             bt             r	  d               ,=             j   j             4                             Z   &             `u             :  
             V   &                 y                
   E                  K                M               \             8                                                    Q                          $                   0  .                J  (                                                              L  6                0j                                                          b                               L   H                                0                               p  F             R2                8     C                                                          T  J                             @  f                            l                          B                   V                               6                ^     '             ^               *                 v,   o             6               R                                  H               >                  >                                (  J             x             Z                t                  !             p0               |  *                               yJ                                6                 F               Z    4             (                  >                  
               `   u             :8                                                                $             0  T                               d               <  .  t                \             4  A                                   .                                              (                                                                                                                           :  :                b~               l               Rx                               |             t             (
  Z             '                  h               d              d  Ӌ             N                                >               v                            x  ǋ                             0   v                                 Ë               
             vV             L  ċ               ˋ                                             vvы             
  I                             *               <                            	               h                    ԋ             2   )                              ܋             $               `
  R             F               R                              '                }                               &                                               j             L                                
             lϋ             w             *  KI                             h                 l                  ΋             `             (  ~                           P    dD                Ћ                R               V             *J	                               ,	  8                                                                      fҋ                          ɋ                Q  ؋             T  
                \                 >                            l             Ɍ                (             Ō             v               >  Hi                             8~               lό                Z                   *                "                                   	  ٌ                            $                  \	  jI                                                  Dl                            P             4   z             	  L                ˌ             4܌               Ì             t               J                                                               F  ̌             \                  \                                           b   t                                Pi                ׌               j                                 	             r  &               +             LL                                                      v2	                 <I                             4   v                   <              I                             ~                  l                
             l               ,   Ռ                             p  n  ݌             8  D   '             J   :               I                -                Bߌ                            *                  i                                               ~,             $                    Č             Ό                                                      ^6                 Ӆ               ڌ                          6                 +,                                R                x             `  n  /                                                       
               6  j                               N|                  h	               X  -                          :               8                R             2                N                 &                               R   2             b             $               0  :               JT             L                                 '                          n                 j                                             r   d  ) 
            ;o                 L                                 )             J                            ^                               t                 6                H                2                            <  |                          n                             v   i                             ,  t)                *                                              <   "             0%j                                                                   T
  4             $                                             Z                  	                                             <                ,                d   $             $                                 3             v   .             d
     .             jz               >   P             &                <
                 R                             "               t             ~  ۔             *               ZY             2	  ~                                  P                              ,                                  6                              BH                  I             T
  e             .
                              8               ^             $   '                W             
  r             4  	                ɔ                ݔ               >{             *                >ߔ             b   	                                                                 ,V̔                  "                               ~                   Z               _             V     @               ϔ             
  d               Z                 j             "                <                
                   <             8  .                             D   	             J
                 D"                               2               ,                                    8[(                                          :                                            $               8               z	                 J                           P             |               v   
                                `                  	                  0                 r             D             T                                  J                  (@                                .               0                              d                                 8                          ,`                                           j                  l   `               p   )                                                (                  R                          ~  !             \  b                               
                                               
  (                            b   n                  p             Z                :(                                                       6                    k                             PJ                             Zo                                                   .                                h               H                 
                r                   :                #                             |Z                P             ~                                   "               d  z  ]I                                                  >   FA                                    \                              x  r                                L	  J                                               JxJ                	                                                                                  ?J                                   d               x	               b   8	  !                x               (                               ,                d  &                 [             F   ^               :A                                     L                9             n                   
            :<  ;o                 	  <,                            I                7                 
            $   ;o                 R  C                            X               VJ                   -             `%                $                 )             T  4                               Q               .   J                '               \                              j             :   @                  U             l  4             I                   x                I                                bJ                                             k             ,                   6   T|I                             ,     >             <v                            XA                   u             P:             A                                               v\   cJ                                   J                             J  0J                             	                               \  E             )             f                               \                 1             D             `   "             	  c                            ^             B             \     6             t*               i               xi                   _             `     @                          6D                                   	               d|               >             |   w             >                                3               )                             .	   
            ;o    g             .e             v   v               P             b`               b   b   9               ')                N             ,@  C              x             p             v             "$               |
                            a                                                  x   `   z               pD             `
  L\             .                  N  d  S               XG             *               hP   Y                              j             ,                J             >W             05             h  \  r             @   t             J                y                V               
  dQ             8  {               <             v   *  x                            b     d                          t                 J               ?               f             L                     <                               .   |                |                                            Xc             
  ~             	  Ӱ             "               -   ְ               ܰ             ~8  a             H                }             6f                          <                               >\`               &y             f   ٰ             8|             J   X                                 {             J.                          .                                                 :ɰ                             l	  L   ˰             &  t                b             0  
)                m               Rð             <  l             6               X    D                             \Ұ             6                t                  D               ,q             B  {x                *                >                                    A                               ̰             x             6k             H  &                 2                            P  .s                          
                 I                                F                                               R               B             >                                  4J                 ԰                  _               Z                                    
            *   t  ;o                 
  B             r      D                                            l  2                dTȰ             f.; X         P       y z Lz hx y y Ly x <y Dx y Dy z x |x tz     Xz `z y y tx 8y x y y z y |y x x Pz x x pm x Px lz x Ty y     xx Dz x @z dx y y (z x ty  y y y z x y y x x <z y hz y ,y dz y lx y x Tx y 4z     y y Hy Hz x 	1 X         P   9  4 ؂        d     x     X 4 H l  ȃ   p d   $ h *       0          P H  t `  (    @  L ( <  Ȃ    @ ؃     ă Ԃ          D ܃ ܂                                     {             Xp   C                                 ģ                P               i                                fˣ                                         l  أ               ͣ             t                  D                                0                               <             @  Σ               ߣ             "٣             *  N             x               |             \   F                ,  V                 u                                                                       0>               (                                  x                )                                h&                            X                  d                                V                `	  y             z*                                 2aa                             .	                   &                            r  ƣ             T  >                8ڣ                              
               L                  $      £             z                            
I                                  ԣ             
   Z                ^   d             r                P  v             &               0  qD                                               @  L  ף                s             :                Z                                               գ             "s               s             L  d   ~                   (t             l   Xt             HFJ               I                I             *  h  J             4   ^.                n.               .               .             .             JF  .             n  }.             H   .             h  R  .             ,,.               T   /             n*   /                .             R  .               /             .             p  .               .             F   .             Z   .             @  .             0  .             ,,.               .             >  .               <  .               .               0  .               `.             z  .             X   6.             n   .               .             .             4.                .             4B  .               .               .             .               .             B      /             2   .             ~  .             t              0b                               `  H                X                   E                    ;                 ^DD                M                C                    -                           ,  Y                               F  R             ~   &  D                   8              r                l             4   &                <             @              \                                               6g              D                 8   7D                                                     C                  9              ^   B                $              f  .              0B  %                	                   "              l2j             |   B              t2                 L              
                                  D  Q              X   t                *                   j              <=                 PD                   I              r
                 )              $                  d               4_              X    c                             z               D             l             b  z                          j               f             n               v                                                                        4                               V             J               "               
                              &                               ^             j
                                                                          X>                                ;             f             d                                                                                                          n                                       ,  \                              
  <                  d               "                                                                            V               6               b               V                                =                \  :               
                                 *                               l               ~                                  (v             >                                R               X                 v                  
                               T  p                                                        h               8  L             "   @P             dj                                p)                #             T
  -                                                          j                NA)                                               M                               N                          "]             L  6             R  [                          
  0             z   w                                  5                               B               
               I                               <f             x   ,             B   Y             X.                               J  +             <	               r   ^                              jR(               	                            8      J             L  j  &              
            *  ;o                 f|  ^             ~*w                          H               h             e  .                `   
                A             
                               |:                              d  %                  (                @               Z7             J               r
  \             @  2  "             L0                                h               
  /             ~  <                                                \             BB6             ^
mL             bL             B     L             ^I             v   W                E                            l  _             
  >Q             
  I                   b             40             ::                            
               R               2   J                              D                   nR                              +J                	                8 
            ;o                 <                                          d
                 I                `               U             j     ?                f   I                 c             8  .	                             &                  v1                            
`   H                !             ~  H                          j  Y             t               J2  I                 S                 L                               @             |               H^             z                 :               p     /             ~    V                qJ                    :                            Z  )I                               T             t'                            2      
             `
  =             4               H                7             <             	     TI                               aJ             	   	                  i             6;             4   N             V   4             |    B                l   SI                             RW             Nd  *             l                b               L  I             \             dI             k             ]             L                   zI                                
  Z             @  2             H   2               dWJ                2                 2             *  1             >  1               O2             n             V   l                   h               d             n                            (
               B                                4               2                 
               $Z             zLY               K             (   <             ,                                                    V   2  V                             ~             &   q                p                  @                            :                 *                $                                 Q                              <                  Z                  n                               ]                               6   z2               :                              P  F                             B  7             >                             @             F                 B                   U             X   <             Z                                             B                             L   {             z               @   a             Z               F2   @               ~             H&                                             n                            L
               ,                                               $                                                 V3             l$x                3             `n                3                3             J   w                   3                hF X         P   7  X	 	 	 	 	 	 @	 	 	 	 	 ,	 x	 	 ,	 	      	 	  	 P	 	 ԟ t	 X	 p	 t	 p	 	 	 	 0	 d	 	 p	 	 	 	 @	 	 	     	 	 	 	  	 	 (	 	 	 x	 	 h	 T	 	 	 	 	 8	 	 0	 \	 l	 	 t	 	 	 	 	 	 	 	 	     	 <	 $	 \	 	                     &               H  ^             8               0   ~                 *~             H~             
Q~             k~             B  W~             j             
    p                 p 
              b	xj	                   i                            N                   |             6               J                 :    X         P       tX dY Y Z X W  Y Y Y Z X Y Y 0Y lX     @W Y Y PY Y Y (W Y V Z X @X Z Y Z \Y xX W PW XY W DY X X     ,X X X 4X W X 8Y Y X X Y Z Z tZ pX @Z X <W Z `Y Y $Y Y W Y X X Y <Z Z  Z X     \Z Y V LY `X    M2             $  1                f2             Y2             >1             tL  1               x  1               (J                1               S2               +2             r     2               2             *  ?2                V  l1                %2                  #2               <2             T1               Xe2             =2             d  2                  62             \  2             1             B]2             J                V2             $  1               2             1               B2             |  81             ~  I             2             2             n      2               F1             l1             Q2                   2               1             $   \2             :   1                   1               2             p`   -2             lx`2               T)2             &  (a2             .     1             b  J                2             "  Z2             Z2             l      D2             v  X  12              1             \     2             b`22             .\  52               *2             *    2             |1                  ;2                0   2             
J                   E2             x   g2                 1               F2                 f  I                1             _2             p  B   2             4  -             <  f.             H    .             T  ;.             "  A                   -             .             
  a.                r.             H   ^.             \   -               2t.             2[D                -             l  .             
  .             6ZO.                B.                eJ                   _.             &    .             z   -             H     7.             B  w                W.             !.               8J                d.                C                
   L.             .   SJ                6.             4A                   5.                 H  -             V  U.                J                   .                 .             4  %J                 .             0  J                   .                ).             BV.               .             $  TJ                9.             nT.             b  -             ~0   Q.             @     .                A                   ..             I             6  *J                v   I             
;J             >\  J                                X  I                   I               I             H      J                          "                 ry             P             <             U	  ; X         P       ,    `  , \   < h @ x x\      l  x  ,   l  P ( t X  (  d  $   t p      |   < h   T ` @ H  L 4  X  L  d  t   d t   p  (         @                  h{                             <                  |(   f             F  
  +i             lr:i                1J             
     I                 I                J             R   J                J               ~=J               I                CJ             2      o             l  3                3             0      3             V	  3               dU                   3             <  o X         P             P       p       t L      X ,     ,  $  8 D (   P      x  8   T 0      h 4    8 d  d     H 0   (     L      `   l                 x                d               `             D                                 \             8T                                   <             x               >   N             $  G                             d                                               FF               F                             L   "s                d  v             (                     >               ]                `                                           Z  R                            B                   M               F}                 1               ~                 ;                   N                <s                jf                    2w              P	w               s             8  s                   *s             dv             |                  \s             :    u               n  w               T's               s                
w               v                s                %s                {             $  #s             D  s             R  w             \Fs                w             h  Ss             |    Us               ~  v                s                w             zb   s             	   	   Rs               hs                /s             >   k$             w             hR  s               s                Hs                Gs                Ns             N  -s             s                   s               w                  &s               s                   v             >Z  s                   w                  s                r             w             J   `s             F   v             
  v                 s                s             v6s             "   r  w             d  lf             |                v             *  s             4  "v             7s             xbv               v             ~  Ns                 !s                  s               s                f  hf                	   Ps               f  v               s                   v             Vs             
pf                v             V  Xs                hv                Zs             d   s                w             *y 
            ;o    v                r[v             .  X w               .   v             As             8   
   w             nfs                    sv                  w               :  s                   Bs             s                $s             V   vv               z| 
                      `             4   θ                   >             nT
               d                 |   b   D                             |   rD                                9D                9               A                    k               A                             :l  d                                                              D                a             >,  M                l   U             v  x                \                y                            Xl             \  f                 H             D     R             @   %c             Z  vc             8  'c               6   b               #c             :  >c               >   c             ~  :c                   Q)                c             	  6c             c               7c                A                   c               $c                )                   
c             R  b                c             Gc             R}c             ,zc             x  5c               +c             p    
               ;o    b             "  Fc             \  c             xc                  b               qc               H   RI             $   fc               b             ~  	c             <c             v)                   kc             tI                =c             nc                  b             pgc             bFOc               3c                                  |c             c                yc             Ec                H                c               c                :  &c             8    c                wc                  b             	  2c             Ya                c               c               ,   Qc             `c             .  L             2   i                A             z   A             r  SL                B             "  A             
   &fL                GL               L             \  A               A             VA               A                f                {                A             >	  A             >xPL               <   A                               i                #A               A               i             $   A             :   JA                i                A             n   T	  A             n  BL             A             
      A                v 
            V  ;o    AL             n  l  rL                i             A               z  B             ^  A             .   8HL             @tH             ,   A                ,XL             	  *A                 A                |A               vL                  A             
B             L6=L                >  A             :   r  JL               j                                 A             VH   A               ZA                 DL             FCL             A                z  ^L             	  L                A             ~A             &
   9L             &   A                fK               A             j   A                A                   A             	   B             0   A             B   R  A             
   A               0   j/                   #L             @  B               i                   ML                FL               i                 /A                LFj                A               PB             ~|               R                  \             V                             &   F                          X                    <                e             D~             P                l                              b  9                            n                H                 2  8             N  o                                                Z             Z  '                a             t             (                P  {                  w                              +                             8  B  "             P  h             R                          f  v  %              D             
  3             2  N             xq             @   =               j             (  f               :   K             X  7             \  v             	  l   L                 p8             8  &             zL                  x               h                  l               t             D
  @             "1             r             N  ^               _             ~  g               B               }             ::                            
             mw                    -             X  r                                               ;               @                J               f               `~             -   g             ~                f             0  ,   f X         P   hp   |      x   @    \     D 8  , , h  d 0    t    <   T $ <               L ( D |    l ` 4 h    4 (  `             l м                  j  s             h                `0               \               0   8               R                                                
               0             :  0                   Z  v             T             .                *                  n                          l                               h  Y             	               @                                  3             b43             V  3               (]                
   3               d3             xb  3             v  2)                2             R  (                   ^3             (83             
  3             :                  2             4
     3               }3             i3               3             n  3               z3             0   V<3             d  o3             ,  _3                 3             3             N3             v   lc3             
  3               4  t                3             l  3                M3               h)             J3             X<   3               TD                    H3               )                O3             6     3                 3               8h             |   w                5             6                 <w                _             7x                '                             ^               !                `J              <                 ]                                             J  u             .     m             F2d                                M                              }             ,             w                y                4w                1             &      w               V             P   0                7                            ~
  I               B               F`             *  Y             U             a             T  X                :  w                    F             $   6               0  3             V                                              p               \                               jz             `  v             :.  Q                                 ?             (4             S             f  c             
  P   P               |  Hx                                T                              P  r             [             .             `     s                  &                            n   @                  D             hG                                           w                 n                            @   R                             9                               "               l               j     
             	  rda X         P      4 h 4          4  8  ̿     ȿ ,  P H @ @   x  ` h    p t X    D  d          п Ŀ  D \ ,  L  0   <  $    8  $ l l Կ           T  <     1<                  H                $,               bY             <               z             t   R   ;             HY                Y             	,             F  BY             R	  ZY             &<             2   x   I                   .<               J  Y                  ,             d  #<             	  Y             d  <             ,   %             .    <             L   Y                 Z   <                 ;             j     ,               <               ;             LL<             !<             T                Y             ,<             Xb  ;               ;               Y             Y                Y             t  <                               +             ;             |  g<                f)                Y               Y             ~   q                oY                4<             Z  I                ;             p   	<               ,Y                `$<               oJ                Y             l  P  ;             4  8<               <             XlY             R  JY             h  Y             X               5             6  ;             X 
              ;o    <                Y             h   v<                 Y             n	  Y               Y             XtY             b  Y                n<                <             "  <   Y             |   R;               ;                "Y             l&j                   Y             	  Y                   +s               r             tr               Jr               6   r             "   r             
   s             
  s             4)s               x                   's               r             p  A                r               r             <  VH                r             x#)                   r             8  4s               r             	  r             H  s             F  r             (  Ts               r                  w                 s             r             r                 8s             8  r             r             j  r                 ?s             28  r             r  g                    s               :s             l  0s                r               r             8   l7s             f   r                r                             A                   r             
r               r                s             l   ^   r             tP  j                s             T                   r             "  r                aI                
   "s             Bj                &s             b  *  \I             	   s                ~r             s               H  <s             j   zr             s             $	  fr               r               r             <  t             l                  
                 ;o    2                  1J                                              C                e             T  zJ             X                   v             ,   `  
D                   6             f   d               0J  ;             ~C                x             z    r               ~               \             0X             X               ^D                                  @             v   p   h             <  D                    q                 l             
  A                                  j:             6                  9             v                4               t                             I             P     b             zg             f             [             &                                    T             |                            h   j                l   7               Y             4                                               J                               m             B             ,   P             V  A                W             N                  L   <             h                  |  d             p   p             W             z>                 ^s                               |               <  d                2   C                                x   
  o             4             C                    y             `  l5             H                                 *  x                                                          nl  2                                             |             (                f                 RD                                H   @  $                 J                                p                               ^             x  ]^ 
            ;o                 6                      L               R               j  /               d3J                             hn                 B               X  wI                                   xLH                x               i                                                              s             ,                          J                                    H                             ::j                                   `v             R                  H                                ,                X
               p  p                  d                d   B                                                N  zI                             	  H                             v   v               H                                                 w               8                 8   -                t                            8  j                                |                
             "V                \  H                r             
   (                @i                   Z                )j                                    i                               I                   }             l  I                             I                             `4                            ,                  &             0               QI                                              p             ,   z                               
                              `                ,  H                                 h  |             p                4n             "  I                             @Mj                             ~                                             <               v     %I                                 @<                            P                 ,A X         P             t     d л   ( 8      ܼ      D     ( |      | H   м      L Ȼ 0  x p  <     h  X ļ  L l  h T \ 8      ػ , \       $ @  T <r d{             &E{             fL{             4  H                   {             2  [{                X  {             2  J                   G{               v{               i{             (      {             |x                }{             "   xZ{                B\             Bڑ             ={             ,  b{               H                +{             "  Z   ^{                 R{               :   1{               {               {             >  A                c{             <H  r{             D,                   z             D	{               f{               `)                    ){             p  {                9{                Fz               {               {             h   8{             "
{             VF{               $t{                `   {                  2{                2&{               /{             $I                   s{               bA             -   {             V  Nx                2   '{               i                   !{             $  p{             I                _{             X   :{             	  u{             
   "{             H{                 %{               {             $  H                   h{             :   V{             "  U{                {               n                 {             
    O{                  I{             t   N{               (W{             j  g{               `{               h{             4   l{             f   B   0{             D  H{               :#{             "7{                                   A{             2jW             XW                 W             R  W               TW                bW                W                (                W             X               9H                 X                Z             	   	   W             
   W             $  W                W               W             X             W               W             ^W             .   W               )                W             X             fW               W             XW             ,
  X             W             .  8   W                hD                W                  W             &  W             ~W             N  W             X             	  W                R  W             2X             Jj  W             B   
X             l  	X               ^   W             $  W               W                W               >W             J                    W             ~  W                z  W                *W               iW             <  W               X  W             W             h     W               8X             v
  W               (X                 X             2  W             vpW              D	  )                   W             .     W             4W             <     W                v  W             ,  W                   ux                W                 X             W               W             X                ZW               W             &  X                )                W             ۓ                œ             6               3 X         P   \		 	 |	 	 	 h	 (	 	 	 	 @	 	 ,	 4	  	 T	     |	 P	 	  	 	 	 	 	 	 0	 L	 	 	 	 	 	 	 ,	 l	 	 	 	 $	 p	     h	 	 	  	 D	 	 	 <	 	 X	 	  	 t	 	 j D	 p	 	 	 	 	 	 	 p	 4	 	 	 \	 	 	 	 	     x	 	 	 \	 	 q X         P   T	 ܡ    T d  l H 4 t  ܢ        X    Ģ , 8   <  \ L  x (  \ 0  Т         p   D  X С  (Q H ء   0       $    l p D  X `         P @                   Z     ݃               :ʃ               Jm                               H                                            Hv               <ԃ             f             ~             2                4	  t                               B  pA                   |             :             .   D  )             !                :  6               Po                v             
\             L  )                                  6u             \                  ~                          x                J             2                  "z             	               
                                                           6}             j܃             p   f   Ճ             :             8                 J\у             
     l             F               :  .                |   >	                 ȃ             P             X   <  iI                                                                |   s             ~  S                                             |                  ҃                          
  ǃ             h  q             .B                                             p             "  B  n             Z               8                                                              ك                               b                  B                  J               <I                             X                Ʌ X         P       T  ̍     ,  4 0 \ Ȏ `      h \ ؍  ܎   ̏ P       l t  @   | h |     ԍ     H ̎ Ԏ ( T      ď Џ 4  ,      d ȏ  8 ԏ                              h+             (                                                \               .             0   	               6             9             :(               6  n               h               
   
            ;o                 J  r               -                                                         $               l                     0                    =             *P             f   h                    5             z                             l                r                            @                             n	                                <  2             @                   A             &                                              |   j   '             1                             z     D             l  7                
             #             ;             T               v                      O             L                d             P  x             l               <F               0             (             B                                             ?             (                                              L                     >                            V                     
                            l   j    X         P      $ % % & % t% $ % @% $ % $ 4$  & % $     `% \% <% \$ $ $ x$ X% $ & % ,$ D% % % $  & d% % l% $ $ % %     P$ $ & % $ % ($ % $ L% % $ $ % 4% p$ $ 8% $ $ & % % $ $ $ $ % % (% $ %     # T% $ $ P%  (  X         P    ,9 7 48 9 7 8 8 8 7 8 8 8 P9 8 8 8     $9 d7 T7 87 `8 8  9 H8 8 \8 8 $7 L7 9 8 7 @7 7 @9 08 7 l7 8 7     8 d x7 8 (9 8 8 8 t7 $8 T8 7 09 P8 7 P7 l6 7     `7 7 l8 D7 7 8 7 7 (8  7 47 7 8      8 <9 7  8 X8 Q `             J                A              F                >                :                            4                 F                   #              	               ,
                *  <             R    4             
                               ~(                                          X                  p              &   	               9               0                              b                :                $  Z                ^                             b   T   )                                                                              b  b                 d   0                 B                ,              ~                                  B                 d	  v   &             |                                                             6                 	  ;             `    7              
             X  @8             \              <   :               >                 .             
                <                                n4             r              :               r                 8  @                5                                          -             X                ~0                   .                           l
                                   HZ                               '                2                p                                                               Vn                ^               ,                |#             \                0  )                                          n                    d                             H  H             P                  j                                d+)                                            j               ~  N)                !   5             	                                           @               j                .             v                r               J   )             "   9                            N
                  d                Z(                                j'             
                               |   l               (                *                               Z  6                            |  (             .  <                                +                x               )                             r                 -             
                 )                ;             z               ~(                               J               |                                  6)                               :                   1             n@                	  b   :                             ,  (                                  d )                             d"             p   T                  <             ^  (                                t  2             "                r   )                               )                .                J               Fx                
  (                   6                 -                -                v-               4   =             T   s>             6  P   -               3               3             03             \  j3             @ˈ X         P     i xi g h Xh h |i h 0i ,i h th 4i ph g h     g Di 8i h g g 0h ,h h Dh xh Li h hg h g h 4h g pi g pg i h     `g h g g g h (i i Ph h g h h Pi h g g i h i hh @i lh g Th 8h h h (h h \i i     @h h g `i g  ˸r             T               (                                  $   `             b  I             zI                I             I             J               I             :  J                I             BN   J             V 4J               J                               
                
  /             >                             p  "                B                                                                B                               z             P               0  h~             B   (               p*   k             4   p               n               N8  %                                          v                |                             t  4             	   	                F                L               @             `                  :   z                            j                                              D                                  
                                             8   	                                                                                                                 l  L                                               H  v                                  &                r                                  
                     4             (                &                p                
   T                                              *                                 v  (                                                :<                   h             .                                                 l~             h     p                                                            	               f               ^                                              T  A                                                                  H  P                               $             "p                 Zs                             D0             6(                              8   G               o             :   g             $  ݐ             4     ؐ               ސ                ǐ             X   	                                              p             
   R             .   ې             \W             X   .W             N   cW             c             6<b             .  0  b                  b             (      b             (b                b             f  b               @  b             :  &3               v3                (             	   3             n   f4             T  3               ^3               3               >4                j                  3               3                w                3               k(                4               	4             3             3                
  3                2  3               3                  )                3             `P  3             3             M     3             .   3             d  e)                4                3             P3             F   3             03             v   `  3             b  3               n3             |   3                           |
  )                                            ~               
               n             b                  D                

                                  2)                                )                                                               l  )                                N               t)                                            H             td               )                          ^
  ~             4                   B.  _                                   y                          <                                   ||                                                XNq                            N                             4                                            P:  
            ~     ;o                                                               np                                H             ~   {                              >                  <r                                                                                                                       L                                              "  "n             ^               h                              $c             xb  2               0               Z               r                    xJ                              J                                               8              X         P             h    Ы ,  p           L t d  8 | ̬    ̉  T  |     |     ī    X   D  (   @    D  l H P   p ت P 4 ĭ     P h ܫ     d 8  \ $    3               H3                  3             &x                3               h                3             ^   3                3                 3             bjnb X         P         t D  < |  p t P    L \     @ d  x 4      x  l    x      h        L   `        L       t  X  |    4   p        h X d     / X         P   d! \ / (        "       !      \ \  #   t    <$ B !  D x "      " (          <   ! D   @           \!       !   !     !  t"  "     D     !                                                  H               ,                               $               `                     I             F  zI             p2  
J             \  I             X  H                    I               I               6J                    J               `I                              
   4               vL                  fM             ,  L             .,  L             n   K                 s                }L             L             t    s                bL               Ts                Q                L               NM             8  L             2  L             0     #s                L             0   $             ,   ~k)                $                $             0$             4@  v(                M$                 $             Vr$             
  V$               )                   \$             $             P~  r(                u$                $             x   $               L   q$             v   T   J$             DX$              r  e$             X  .$             F@             $             
  (                   $             <  $                 $              $                x   $               ob             d               (d             jd             i                d             >  f                   d               hd             2d             $  d             2`  od             |n  d             &f                 qd             (  d             <e                 d                d             p   X  d             &  8  d               d               ad             F   d                d             *  4d             "   4  d               dd             d                zd             pt  d                p  d             ^   rd             n  vd                -o                d                d             &   ed               d             d             .   98                ~   7                7             x8                 G8             d  7             lB  7               I8             
  8             (  28               58                6   @8             n,8             :  7             
  v8               6    8               7             H   t8             .      8                l  o8                  7             @     =8             2   x  7              8             f28               X.8             47             Xf  U8             7             |   0  *8                 38             (`8             &  8             r  H8             :  C8             7             :  l8               8             <    7             <  h7             FF+8             <r   8             j     48             D  7               
7             ~  8             8  8               \  7             2    7             h  E8                  f                   7                  7                   8             H7             08             4  18             $  7             7             8             8                 7                  8               78             h7             /8                7             6v7               "7             j   ~   7                #8             z?8             d4  v 
            l  ;o    7             7             7               f7             t   7               F              V, X         P      ~ D 0 }  ~  ~ ~ ~   x ,~ } ~      | ~  ~ ~ ( ~ `~  }  ~  ~ } d ~ ~    ~ } `        } T~  ~ X  ~ ~ 4~ }  ~ d~  <   ~ ~  h~ l~ t~ L~   }  l ~ P~     } ~ } t  ds ŉ X         P   o	h ,  |  <  Ȑ  (   p  t t        4 l x  @ 8 l  ` d đ   T  4_ L           P ` \ $ А D | h   t    P  4 Б H d \     (  $  X ؑ     8   x 0 pr	             .                  !             j                  +             .   p                t  -             R    C                               ,                                  (             <                   
                                 J             E             $                @   R             f   r                                0                                      8               j@                             $l=                            h               L                            v                    4             6H               1             $   F               B             
  &                
             R   j  %                             |  2             |               \             *               8                  ~                  5             `                                  P             *hP                 
              J;o                                                  ,                                           /             J               n               9                (               (               H   $s                
                  :             B                  G             Nz                  V   l               #             L             
               P   B  ;                                          ,   v             V  ~  v             "  gv             0  rv               v               v             *  av               v                  v             4v               cv               \  s                   v               v             _v               nv               tv             0  Lv                   v             P   v             *   v             bv             v             T  v             
Bv             4"v             >v             jPv             J0  v               v             `	  bv               v               Zv             ~6  v             t]v             H  v               v               $w             D^v             X   kv               v             z0v             v             
   Jv             n  v             &  ~   v             b  yv             X  &   v               rv                  cs             8  v             Vv                 v               v             .  v                   v             j`v               v               8  v               v                  v             v               v                 v             rv             mv               P   i 
              F;o    v             v                v             ev             V  v             6  {v             v             ,\v               v                v                   v             $  6             r   0  K             NRs               #                  2               Q             (  i                   f                |   8             R  fD             ,   |                   Z             (  H             f                                 &   j  L                  f                	   q             f  f                   T               0  Cf                             2                  L1             $   g                          \>                  f                h               \f                                 4                              Z     f                +             .  0                                            N                              f                *  z               s                             Xm             |               ,             z               $   4   e                N             &  yf                    (               Z   G               |J               x  S             l8l                          v             Pk             :               j4  
             z   p  f                             N  .               @             ?             c             VP   B             &             |   |                                    	             J  p$             pi                                                 j                          4  =f                <             f  `                  t             R)             T                   x                y             (                     u             
  nI             dd  J                    DJ             :   I               I                   J               &J             I                I             &   v   3             
3             F  3             b    3                               3             
  T3             :.  . X         P     $ p <     |         |        T    d 4  0        x   H x      x     4 D  8 0    P h l   , h  @ t     t  X @        p    i +             6   /%             8             F  (                
               j2                
   L             "A             ,  ~L                  "s                L               tL             JXL             &   L             hL             2  |L               2   s                oL                .s                   L               UL             :l               s                    jL                <6s                   aL             2      L               H   L                 pL             @   M                             h  L               o~             @   L             $  H  L               8L                L               H  !s                _                )s                V                (s                
   L             Z   z  :L                L                >h             &L             R  `L             jvSM             n     WL               blL                L                i 
            .      ;o    L             X  L             .   L                A                's                L               0s                L             p               L               s                L             $  L             ,  L             V     L                2s                   kL               L                   s                A               b6L             "\L             "   s                L                   .L             0  Z             "   L                  J             X	J             JJ             ^   J                I             xJ               `v>                 pM>             |ϐ             -             tj-                2-                 4 X         P   A t\ p] [ ] ] \ ] \ ] H] ] ] \ X\ \ xZ     P] ^ \   ] [ @\ d\ \! <\ \ ]   l\ [ ] ] ] 8] 8\ 0[ Y D]      @] \ t] [ ] ^ @[ [ [ ^ ]  ^ [  [ (\ x\ ] \  ] ] ]   (^ ] ] \ ] d]     \ (] ]  \  H? X         P       	 	 	 	 M 	 T	  	 t	 	 T	 $	 @	 8	 	 	     	 	 ܑ	 	 	 	 p	 	 	 	 	 \	 L	 $	 (	 P	 	 t	 	 X	 	 	 	 D	     L	 Ў	 đ	 	 	 	 ؏	 	  	 T	 ܏	 Ď	 ȏ	 8	 $	 @	 	 	  	 ̏	 `	 ̐	 Ē	 	 	 ȍ	 	 	 	 h	 	 8	     	 	 	 <	 d	 Y	T                ^               &  4             n  ~  3                 3               9)                   3               $  K                   3               B(                3              X         P    	|  @ 4 l   p    L         D ` \    H             p           P L  h `       P         p  ,  d 8    4  8     \  |  T 0	 X         P   $ X  t x   $    d 8 L t  `         P ( H    h     p \     T  ( (     8  4 4     , 8  L  0 l  X  ̨  4   D < p     < P        P   
   F             *             
  p                                             X   
  I               I                ?J             F  R   I                    I             <  I                I             F  J                I               ^  
             \                              h  =             2      <>             4  A                ;>             ^x>             P  3 
            *b;o    @>             \  ,>                 i>               J                   L>             N  I>             p&A                =               k>               ^   J                    >             0n  =             l  t>             XB                    =             .  |J                =               &   ?>             ^:>             =             h  />             >              >                h>             d  C                   =             =             ~  3>               =             4  6   _>             ~>               A                )>             N>             8>               >>             <  J             >                  #>                X  A                   =             j  A                >             v  t5>             t  D                   >                >             x8                +>               T>             ^A                   =               8>             
t  A                Q>                 =               &m>                =             4     X>             zP>             *>               ->             b  Fc>             
   n                 3 X         P       @  ,   ,  4  $             d  0  l P  l  t  `   $ X  h ,   x  | `      4      d    0            P    @ 4 T  X | 4 $ D t      p    <    ?                :@             *  &@               @             *?               `@                j   ?               @                (?             `I@               ?             
     ?               .@             9@             @      )@             \4  ?             ,@             G  C@                  %@             d  ?             (  B  	@             B  xJ@               ?               ?             `   ?                B@               ?             (  ?             2   l?             ~  4@             B  6@             F  8@             "@             L                   Ӷ             V.                R  Z   -                   -             ~  t-             D  -               -             z-               -             ~     }>                 -             N-                <               X*              4             ,(                   
            Xh          ~3             
   t   3                                 3             ~   K3             <  {3             6   %                N3             ()                y3             |   ^   T3               L   (                    -3                [                r3               ~)                3                 D                &   53               S3             2  \3             X  <2             x<Q3             Z
  	4             3               (                ]3             J  2             J  a3             \  3             v  X3             r=                   3             B  %3                O                73                3             v  :3             *3             zL   )                    V3             J  s3             4   A  u3                C3             M                B3               D'3             $w3             2  mD                   2               3             (3                ID                 W3             <     (                3                 3             *  @J             2   3I                I             (  I             FI             I             e                              @  4D                                   &D                 R              
  <              .                 4x  #                 d
  C             
              "                   D                @<                >              n                 f              *^              x&A              v	  m%                N              
              ,                                "/              @  V                                   kD                V              ^S                n6              r  v              5                 1              r@]              : 4             3             23             r  4             >  <   (                   3             b   $  I                                t  /                                    6  l              \"              |  r                                (q              v  M              |                                                   y                 NF                0  X                 s                   `              6   P                 b                $   5                T                 
   ;              .                 (   2                 z              LP-              :   t              L                                   `^              
                                   *   E              F                 W                              4                H                J              
   20              J   v  
                 Fi                 k              z              2                   F   6                                               F                   | 
            d   &;o                     !                                   8              fz                                 G              X    g                n                               (                                X     _                 B                ,4              :  L              $   U              0     	                M              N                
                zy                -             f   -             Bh  z>               8  -                 d>               D                   -             L  =             h  h             Z X         P   , K K (J K J J K J dK K J J K J K J     @K ,K pJ J K J K J K I 0K J J J K J K 8K  J (K J K J I     K DJ K J $J 0J  J K K HK J tJ <K |K DK K LK K TK HJ K K @J hJ K J  K J tK lK I <J     J 8J K K I & 3             j  ^"C X         P     P X    <   T   t        4  8    d p   @ H   | 4 D        T D      L  \  0 h   @     P    T ,   $  `   p    ` x         8 $"                              >                               \  W             I             I                I             D  n-J             |  I             6  J             +J                                              .             +  .               .                  .               t> 
            b  ;o    .             p  .               .             :  .             .             6f  .                8.             p  .               J                .             .                X   .             .             f  .             6  .             .               .             (   h   .                b.               .             :  .                   .                  .               .             <sx                ~.                2.             2.                 Z_                !_                '_             B   ^             J  _                  ^                 p_               b_                   
_                  (_               q_             j     n_             F_             f  @   ^             O_             ^             JP5_               t_             f  _             f    Y_               m_             |  d_               uG             _               ^             ~  _             Z  _                  ._               T_             N_             2^             _             :   _               V+_             j^1_             F  &_               $X_                   D_             Z&   _                _                  @_                X9_               ;_                 6_             Z_               U_               =_             v_             PC_             xo_             j-_             *E_             ^   /_                 j  a_             |Jpd 
            ;o    _               ^             _               _               W_               DI_             Pg_                V_               ^_             F  b                r  b             0b             B$
  b             $b               vJ                   b               b                c               dJ                   b               b             "  fb                
  b             (b               &c               b             bb             @   b               b             ~  |b               Jb                 c               J                c                .  AJ                &c             f   R  b               Pb             ,b                8  b             ~	c                b             $c             n    b                  b             
    BJ                #c             .   c             b               8DJ                b             0  b             b   `b             .  c             D   b             V   b               p 
              ;o    b             .B  b             b                fc             LJ                   b             .   $J             b                b                b                \  <J             b             b             b             6  b             jc             b                c                b                c             b  8   5J                    b                
  b               c             @J                   b               J                   b             l  CJ                b             b                 QJ                b               = X         P    v	ԧ P  P       T    ̧ ܧ X      x    (  p d   ܨ    ` d    p l  ب      4   |  t    4 L   t  |  X   p D ̨ l    $ @ H   D      ħ  |      w             f  d             d             0   d               ~f                d             &   1  xd                  d                d               d               'o                   d             f                   d             d   dd                 d                ld                r  si                d                |d             "d             `  P   d             d                  d             $  Pd             d               d               d               d               f                   `d             jsd             ,   d               d             $    {d                  kd               H  i                d             d             T  &  d               r             H  z                                
  nx               `Tx             N  x               |Px               D   @x             (    x                x             0
   x             
     vx             x                   x             >   <dx               D~x             4     jx             z\ux             ~  x               x                x                Jx                y             &  x                n  x               Gy               2   x             Hf   gx             BJ-y               y             h     y               x             f  x             L   F  y                x                Yy               x               `x             r  x             x             ,   ky                y             J   x  x             x             8   (0y                ox                ax             2j\x                             "\x                D  y             l  x             b  x             (   >x               
  y             
  gy             `  x                  x               x                ~x               y               x               x             
   0Iy             T  %y                 \y             0  ex             
   }x             Jx                  x                x             8   x             vx             vmx             8   x               x             N   x             *  x             v  x                ) X         P   j  p    P x ,  x   @  \             h  $    T X   0   l `  <     8      ,  p      T <  0  X  8   0   `         (  d |   P X         P   	   H   d    T              @   D    $  <                  @ ( t      h X     8    d   8   p x x  (  H          L    h X         P   }       L   T D h  H  <          ,    | X P    `  t X   d @ x       0      4   |    $ t  P  L     T      < H     `  ,   < |               L   |               4|                s                |               |             &s                |             *     f                |             |             |             |                |             ^  |               |               Z  |             b  s                |               |             R|             n|               |             h                |                  |             J  |             z    |             ,   |i                   y|               |             F$s                |                Z|             h                   |             <$|             ,   
   |             ^  s                   |             |               v|                  s                |             }                |             R  `  |             H  |             |               x|               |             Vs                   5}             *    |                   s                |               w|               >   |               |                 |             H|             >|               s                   |                  sf                |             ||               |             }i                |             .  |               |             R   |                 |             (  De                |                |             :  s                |               |                              s                |               |               |             t  |                |               h|               |                  {|                j|             t  |             l  f                |             @	  |               9             N  jr9             89                 9             <9               m9             lL   9               *9             :   X9               e9             *  |9             F  9             x  9             Vpj9             6z   9             9               lf                9               9                 9                9             @  19               f9             j   9             p  9                vo9             i                9                9             |4  z9               ^9             kf                9                  <9               ^  $o                9             &  9               9             "  tt9             9               F   9                9             6  s                9               c9             |   9             2  n9                9               9             N  ;f             !      9                 6             9             9                 
f                 l9             j"  9                9               9               9             n  9                d   }9               B  9             
u9               Vf                   9             
  \   9               of                   w9             p.  ?9             x  S:               9             b  :             <  wf                   9             Rn9                9                v   s                ~9             t  s                   9             h  `9             8,  :               :y9             XH   9                  vf                9               9                q9                          j  xPC             0C             R  2             2  K             t  NC                 @C                  g2             ~  (MC             :  2C               C             >22                  C             F  B             "  +C             2               "             d  $2             -C               <C               ^2             v  C                B               j(C               3               :   %C             6             8  C             \o               2             |   C             :  5C             
  6C             V  2                            |   n   9C                8  CC             JB             &             D|12             F  KC             
  Z   QC             |   2             ~  'C                v  2             1C             n   V2             :                 |C             h2               &C             2             |   .1                2             P  2             n<   f3             ~  OC                C               j2                2                #C             |  v  2             C             
    4C             T<   =               6  ;C                 .C                   2                C               h2               2             :      2                 C               )C               2             z  =3             3C                o                 rp             F  p             \No                Tcp               8p             >p             $      f                lp             

Fp             (  @p             J     xf             	   	   gp             <   &o             z   if                #p                 Cp              <  /g                o             n  i                .p                tOp               Lp             Dp               p             |   f                   p             X   Sp               f                )p             n     3p             o                 Kp               $p             ,p               Up             <  o               p             v  N   Hp             ?p             /p             f  p               o             2  !p               o             :     Ap             Ep               o                p             0   %p                 p             (   o             N      f                 ,p             |  i                hp             l  .i                \p             2      o             Jf                   qp             o             f                (p             D[p                Tp             *  Pp               Zzf                o             f                Vp                |   o             H  6Gf                5p               ip             z  Dpp             h  p             Z     mp             D$  {i             
   "p               Bp             .  f                o             L   
g                p               o             `  zLp               `qi                
/               Zp               p             RB  {f                ]p             6  f                   Jp             |             2               6             >  >   }             .  |HX X         P   J	00 0 0 0 \0 t0 0 0 / / l/ 0 0 / 0 0     p1 0 l1 / 1 / / 0 \1 1 X1 0 0 0 0 `0 d0 |/ T1 0 <1 1 / 0     @1 41 / H/ T0 t/ 0 1 h0 /  0 `1 d1 $0 |0 0 / 0 / X/ 1 / p0 / X0 D0 / <0 / (0 D1 h/     / 1 \/ / 0     O             &               2     t             J  "             h#             @              bTB                                                r     X         P   	j l ,l  k j Pk j \k l Xk k dk 0l l <k k     j k k l k l k l l pl k l k l k pk k l l k j $l l Ll     l l Tl l j l @k l hk l ll j xk k |k l j l l 4l dl k 8k j $k (l l k `k k k j     lk l \l k l  	J             P  I             I             Xp   -               -             6-                ~{>               -                -             <?             @             H   @               ?             0E@             ld  3@               ?             P@             .  0@             &  p?             ?               @               ?                ?               7@             h  ?             .`  /@               ?                !@             ?             z  <@                 @             >   ?             $   =@             df  3               
@             R  G@               ?             z   B?             8  F   ?             ?             H@               8  @             h?             Jf  @               b  5@             0-@             &   l   ?             2  @               ?             ~  ?                  ?               @             tl   I             D  fGJ               I                   J               .J             rI             (l  I             H  ]             D                             J                               ,                                                 .             t  \             4   A                             (             t   r   tD                                )               :             T                 v                  G                               3             TB                                             l&               b  u             8  <J                             .   (  u             B                                  T                            (             L                (  1D                               ^l                             x             |   >                            X  r                                6             `                b                               
	             f\               D  6                  pJ                                $  
                0   I 
            N  ;o                 @
  A                             2  D  A                1                              9             ~0                                       T     D                             8                 >             <               6             Z  ,             DJ                .                          f-             
  b   U                          .   T               0               NJ                             N  .                                                  
     %               x                             f&                          "^>             j  {             V2  B             3f                                            R   ޔ                                              P-             b                4             .                  .   Ȕ             *                    d               `Д             0             @Ք             *                  0     0                             >  Ӕ             P             $      W             l  -             &  -                -             V{-             >             t  =               x-             b-             t  R-             v  -               <=             $   -                2-               x>             -             V  -                  =             j-               |-                -             Lq  -             H  y>             x   w-             P-               -                B>             ~-             R  k-             <    -             H  $   -               -                  
>                 <y-                }6 X         P   @ \( <( ( ( ( <) ( ) @( ' ( )  ) ) ) (     0) ) t) @) L) P) ,) ( ( d( ( ( ( ( l( x( ) $) ) ) ' ' ' '     X( t( ' ) ) ( |( ' () ' ( ,(  0( T( ( |) H)  ( P( ) ' ( ( ( ' ( 4) L( ( D( '     ( ' ( ) ' > t             H                0                             8                  f                   $               H             
  d             	  d                                  |             j:                Tr                V  2             6                                 &[.             B   E.             @.             *  F   X.               q.             ^
  .             	  -                  A                   Z.             
  j.             ^   V
  -                .             z  1.               J                -             &     G.             $  "   u.             
  J                    .             6   )                .                v.             .   3               8  '.             .  .                .             tJ                 -               -                 H.             (  p.             T  .             
   .                J                %.                  
.                  {.             `"A.             ~   -                              s                                hs                                  R                r                 x             <               bV                 P   s                             B               :P   \               s                                                   s                                 ,  
                f             |s                                                                 w             v               f             R               jf  n                p                ~s                u                                         @Lq             ,   s                               h               8s                [               y               $N               l             2\g             R$U             p   ^             ^v               lD                                             N  D                J                p               8<             T    s                               s                   M             N  Q             bZ             (s                             
  o             s                                     s                                  _                d             |  s                    	             j  x                               4    is                                          z               hP                  s                               1             
                 s                                  P               2                6s                          4      j             h                   ~   s                                                 I             ^  H               R             B                   8   G               C                              x                                            0  S             .  -             ,                O             V                               \                     T             ^     D~             ^  3             f             >                 ~   ,             X  |             ,  :               ~/             2  n              ^  A             >z  c             |P               k               2                             X  6             h1             P  _                              d                                *             *0                 z               m                          |h                                  I                            ~8                   L              M               J             "      F                 #             >  T             j>)                          z  ;               N   i             V     ]                            s 
            8  ;o                                .               0      7                          &  @             NK               
l               "             V   f                                 J               f                  +                              !                            B  <                             > X         P       4 $ D  ȭ p  @     H      ԭ < ̫  X h   ج Э           ȫ ī ح l        t  h l Ĭ x T   ,  ĭ p , 8 (     ԫ P  Ԭ L H ܫ  4 ̭       ̬                      k                	                 J  w                            >t               Et             (  Rt             p  at             (      "t             z=t             $s             b   Ct                              J   \t               0t               Zs                At                   `t             n  Mt                bt             >t             >s                   Yt               s                Pt             s             s               1t             R"  9t             s             s               &/t             4  s                @t               s             ,  s                s                Ls               j  s                (   -t               s               s               s               t                t             &  s             t             $    Z                   t               5t             0  f   ^t                 Xt             T  (   $t                  t             "      t               s             @  t             Js             R	  t               s               RUt             2  s               s               :t                 t               s             *>?t             B  s             .t               )t             `"h             (   [t               Ot               s                   s             lt               s             2t             ~\s             8  s                t               ,t             |  ^  s                %t             (t               Bt             p  s                t             ns             f<Ht 
            (                                  
  ^                            :8                                  n0                  S             x               X  8             @                  N               h  K             b=                j               $  X             |f                               tIs 
            ;o                   
             v                                                                    J               a             ^  h'             P                 E             l                  h                ܙ             T             0r7               -                  !               ؙ             &                2               |  |  <                b                  W               3             ^  s                2                          V  V             .                 ,             *                               b?             G             L   F                                             &J               J;             V  P               4             z             j   jQ             nL.               \             \  :                 rC             V   #                          |                  R  zڙ             M             \                J
                  _               L   *                          `8  $             2  4&             Fy&               r   &             d  ɨ             6  X^             
`	  ֨             NѨ                               v     s                a                                               z             8                 $     s                             0w             
~               Ө               s                                              Ϩ               ʨ               (s                Y               <                H   ը             x             >  ]                
  ̨             j  js                   J                ͨ             x  s                ܨ                0   b             Z   "  Q             \  ԫ 
            (;o    `             j  Rg                            Ҩ                          `                j  l               s                                tas                   ~                s                	                N  v               c                                
             V             s                   {             V  ,s                |               s                Ǩ             "    s                                     s                          $s                             e             "                                 4s             	                    Ш                          s                T               è             >                       t                  s                                                           `s                Ĩ               \                [             2      s                j             x`s                               y             &  \             xר               s                             ,                    Ȩ                z                P             V   l             n             ū               ի             Z               ~b	               R             4  Ы             v  H
                            <                0&               Pp                             r4               d               *	                    ѫ             J                   	                               b                                 n             t  0             f  vƫ                                 $               r                            >             *   	                ۫             D                 "                H               8    ٫                               .«             R               <  D                                                              r             4             *                  Lϫ             H                                           .  ǫ                              0             z  zs                ޫ                            P  ׫             Pj߫                                 ˫             |               Nӫ             <                 $  Ϋ             d~             ~b                              ~  J                                                                       nk             |             F	  js                             Ns                   \             V   nS             ,                J                r                  D                   `  ^                                Zys                               s                ¹             L             V    Ĺ             4                                P$                            |               os                ǹ                             bι             d                 J             6                 >|  I               6   x               jes                                VV                  }s                             t  Nms             p                  c             B  N                 L              @             d                                    ps                                   O                          fr  ~               Z                  ns                    ͹             Z                  z             n>                 W             .  .h                Թ                             Z  L             
  Xs                                &     s                                ss                3               rs                   b             Z                ts                n               ӹ             (  ds                    ʹ             D             T  gs                v                
                 vvs                T                            f               K                s                                ^  ]             ~  JH             F  q             H^   &% X         P     p  x  H ` X ܳ ,  L    | (     p   ĳ   4     h  $  d l t  Բ  X  ̲ ,      0 ,  4  D  h ȳ     H   \    (     в 4  0  @       P (  T  B             $  h             
  2             I             (               H  *                            P  k             >a             "	  s                             b                 &qs                g                               Tf                j   s                ȿ                          n                0B                                  L  ^s                ܿ                  \s                ٿ             r|]s                                   H             D   ls                               c               _s                
                                    cs                                $  
               `s                                               "  Qs                                            N@   Ϳ             hP   p                 ؿ             ^o             l               rJ  ſ             <      ds                   e             Xw             ,  l                             4  x               $ҿ             B                 z   s                d                          t               j  ߿             (               l             *$  Rs                ڿ             ^    ˿             ^               us                                                          s                j             "                  dƿ                t             ft                  [s                ѿ             2׿                                           `Ss                             n  ӿ               _               l                bs             
                  .\,             n    ο             8               $  n             J                   N                p                 vԿ             
  '             >      v             4z               rK               
                @  f                                           (                  *r             u                            8               V                              Z             l             x             \               8  T             .                            0                v             fT                                           	                              L&               x<                            .h                             8               "             F  v             V  6                                                 ^                 ~                  |             2             v             6    |             4                     T             z                 B               h   
            .f	  ;o                   ,             .     w               o             v  {                                 @                                            r                                   >             6                       q             t  k               b                P                6   n                          
              X               ^    t             J               B             Z                                "               |               h                2                                p                  F             J  .                R]             >               8  B             |                 :                :                l             *             fP                              >  \                                             N~               K                  0               ^               |                                              
:             Rp             N                            d   +             r             2               0                            x^                   \~ 
            H    ;o                                8                   nd               ^             j  x               Py             (                                 6                T               T  o             <               j  rg             T             R                               j    ;                             8                                                                  ~             b                 J                  _             TD             d   f                             45             
   d             *s                1                -s                             \   #             v   fs                                h  Js                 
               ^Ks                             >                                 x                zr                 Bs                                 Z  x  .             n  d             2   t   (             0   w                             &                              
               $                                `               @s                &             :                    /s                                J
  :                             \               r0  7s                "                :s                                N  3             D   |s                                                                             l  F  9s                                 V	  '                            Hs                                F  z;s                                N               >Us                                  -             R      &s                             &             <               F8s                                            	               D     3s                                ^    2              Ms             
                                               (L             $  ?s                          O                r  )             Gs                                                L               VN  8                              v$  /             ,                  `                J               L 
             	  ;o    +               4s                                f  	             J6             ^                   8             h
                                 c             >             X                               T  $             4  6               L   P             >   1             (               4]              9                             2             Ц               8                               p   -             G             (                                              6             6   |             ~0	             n             R  D                            0                  N   i~                          (   2  c~             d  ~             T  ~             &   ~             6  
~               ~             }             X  @3~                ~             ~    @               `~             ~             :~             P2             P~             .   p  ~               ~               ~             <  ~             `("~               ~             6  ~               ~               ~                |  .             QJ~               L   ]~             2   
            "  &;o                 J  {~               p~               4                b~               }             "     ~             }             B   }                j;             2   }               ~             ~               j   ~               ~             .  ~             4p  ,             (~             vr               p~             h  Z~             L=~             P  (~               (   }             .H~               D~               L  m~             |  ~                          2~                   ~               ~             	  }             `   ~               ~             Jw~             S~             H  ;~               z~                  r~             ,J  G	             v                 zv             
$                  6             2               <             ^v               y               0               	             $f  F                z             `  Q               U             x
  )                R|             .             ;             6             V   A             *                 C             ^  z               H             >                 7               \               j             1             4                 0   L               %               \   G                            r  ^             t    "                          .               4-             @   s             
                   3             J    W             0  b               rk             Z  O               n                            h$v                           6             6             >  R             F  
[               ]             u                          V               .   r  l             .  E             .>  !             V  =                  T             \                  &   P                ~   9                            z  K             <,                                          a                P  m             2  V                 o             X             V   w                              &	  Fs                   e               $s                                  S             |             V   s             
   >                                ,                <  C             (     T               Y               N               	s                             >`  s                                  j             ,"             (             ,   8                J               a                     +             4   zs                             ~               J 
            X  ;o                 >   s                   d             XD                j                            vv             H   Q             J             2     Ds                   W                            8  s                L             
    .             28r                    G               m               V0                c               B             64                          ,  6   6               \s                3             D  s                s             R                                s                t               ^                             (     f             l  &             ^                J               ,  j             6  9               P  I             `*  ;             :    `                  ks                
   %                              r5s                             0g             
,s                    }             >                k                s                                d               Ћ             (S              6                                     .  r             ,                <p             ^4                0  ^                                           2R                                  R                j             ^4  7                Y              2                  (             4   >                  4i              F   1                 >              f                X                   F                 J   R                           &                                                   -              B                 8                      g                             `  V             .  f  Y             V     x             B  6  v              *                 l                4                                                L  ^   V                ?                    O              n              t                   r                     I                  A                              M             R>   i                 `                l  t                  L               9                 M                                 8                r                               <  "                   ,              P                6  6   O             5              6  LG              Z              8                	                >                                                8   +             TB             |               H                          f    C                          6  t   '             8                                7             H             Z  P             L  2                            `  t             \               $  v               
                J   =                                X  
                                 (#             ,     !             n                                 R             f                          L                   $             
                 @  $             ,r6                                            D                BJ             H                                  A               E             (                  5               -             LZ             ,               F               M             b               l               2  &               %                            t  @             &             x"
               X                  d             r               "               ,   ?                ^  <                3                                       l&             2  J   >                            `3+             z  +             \	  !+               jV             2   W                sW                TW             l   W             .   *  W               YW                  tW             (  H   mW               c 
            ;o    BW                 B  `W             .JW             :   V             &  J   DW             <      QW               d  1             W                 GV             0V               W                0]W               *W             P  wW             l  PW                             *     )W             T     dW                  W             <PW             z  K   V             t  W             p   P  NW             X  W             W             *   W                +W                 rW             4  ^fW             2   GW               V                g                H                            BV             V             R  V             Z	  V                XJW                V                 RW             W                kW             4  7W             $<  xW                 W             &  W                  9W             &   {W                vW                zW               N>                          *  p               ~W               hW                (W                               ׃             F     
W             N  d  AW             *  V               lW             
  W               |W             0                  c             .w             ^                               Z  4F                            (g                  M                             (	                                  `               Z   ls                   &             L   x             pbb                   _             /~                @                                j                              ((             P                                   N               b             r     
                              s                ;             4    P             H   
s                                   s                   L             q             $               s                          .               b                   \               N                >                ]             D               j                   y             {                            6   
   9                               L             s                  
                   .                                                             V                .                                                  d                                L  `(                                                
                    ws                                              F             "    u                                                   b                             ^  ht                          (               Jc                             D   ~             :  D                lv                             :   Y             `                 ^               R2Q               V             ,  x                             t  |  5                              &                 A             x6*                              F              X                               >                          |                                                       .             s                 @   H             0             R                T                x                                   S             P   X               ~P                1                V  o             h  /                                               "             fg             z                                        d             xw                               8                 @                 #               s                r             Z             6   <  s                ]               U             l                              P  ^             c                ~             (               p             F  <C                             J                                                  n                                                    n             J  L             4                                                             .  -                                   ,                D                            m             *&  ,                    >               <               M             6                                            t                  ;             R  2   N             Pd  '             F                  O                                     7             |   j             
  8             N  w                                     	             B   Dd               c               Zd             l  <;d             >d               zc               c             *      d               c             H   Zc             c               ?d             	  v,c             :c               c             8  c                   >d                 c             0d             .   d                bc               :3d               d             v  dUd             t  9d             b  c                Hd             c                  c               Cc             c             ^   rc               Tc             L  d             m             X  c             B  c               c                c             &  c             L      d               c                  %d             &d               ~  d                n	d             Ed             :d             j  `d             8 
  c             .d             8\  qd             
  /d             P  c             @  ^   \d               gc                 v 
            f  ;o    c             h  c             ~h  Vd             (    Nd               ec               c             c               wd               c             (  Gd             v  -d                  ]d             :   c               $d                d             $   E	             &  	             *     	               Z(	             <  b                A	             t  r                   O	               k	                               	                                  	               S	                ^	             .   V	               	             0  |y	               23	             M	               X	             rx	               !	             s	             p  U	                P	             <   n	             t$s                   	              ~	                                  |	                 ?	             4                   ]	             b   ;	             p  2	                   D	             *                     	              A                   [	             8    	             4
  	             x  n9	             $      f	             (  ~i	               
	             >  a	             n  "	               h	             w	                s                   C	             ~  N	             	  TQ	               *	                                6	               	                            L  z	               z0	             4   NT	                '	             t	             :    	               	              2	             , 	             R  V   y                   v	             \  /	                 W	             7	                                 c	             P  	               =	             >	               N$	                                   	             8                  	                %	                  5	             ,  Rp	             d	             2               :             ^  &               .                                            j                g                >               P             -               0             V               4D  V             f                                                  6             H  4l                                        m             4                   I               A             B   6             o  
            ^;o                 *                            T   ^                               
                 b                                X             h  h             <                  _                 "             j  V   Z                             0               (b	                               '               [             t  >                                                0  0             D             0.<             u                             :                   T                   i                             h                                                                              
  4                                    )               G             >  b                (               %             T                                  ^  $             tp  @                M                 C               3               `^               F             D     H             2@
  1               <Q               :                ?             J      O             d             t  @                               e             0                               B                  a             
                  y             4             Z  U                             ,  j             "                                 @   p               }                x             X	                               V                                 B  T                p                                 `  n             u             `Z                                                R                 :             $                            "                                                               z              q             ^             $                             @P                                 8  f                              .                               H                            V               jL               B             ZP               p                               X               z                                                                                  p               >               $      {             ,                 \               `                                "               &               ^                  n                h                                 J               P   z             @                 t             \               J               H                  ,                h              `                B>   w              T  X  z              4   ֦                
c              b  ő              t   {                            >       
            0  6;o    Wd              Z&                p  "Lh              j  J                 >s              4  ,+                   :              ~             	   	                    m                              f                         S              b  .                              T                (   i                ܴ              	  I              :    d              Z   (v                                                     
                 8                                                      	                I              +              0  hAZ              ^                                  =                                  L                   Q                   c                                                #                              6   `  v                h                            l     ;i              O                                  T                 R                
                ,                                 }             R  '             {d                 V                 H                P   z                RL              {             
                                   Ŝ             H                       
              f  &   Q                 7T                 a              P                     p              
   <                 $                  	   Y                                                Ai              `                                 Z  r>                -               o>             -             d  -               `>               -                ^ 
              ;o                 l  \  4                3               3             X)             B   4             :4)                3             z     s X         P        P    `    p h H T        @ 8       @ T t  4 H 8 (  L   X  $      8 8  p  |    l  d <  D       $  l     \  | |     (  x                 V                 R  k             &                                t                B
                                
                v                :              \  "                P                "                                                        y                                                 J              
                 j                 \X                `                                   6X                 >  r                ,                                               fV                 x              0                P                               .                :                Z                ^                                               <                  4  $                                h                                            T                f                  l              h                  ~                            |  L                <                                                                      l                                p  
              *                 V  n              n                              `d                R  f                 8                *                   P              "                
                                J"  !                "              >  !             ^	                >  f}              ]Z             H  %             ~  ,                ,Й               ;             t                     R             V  zo                                                          <8                                       	             *  W             T  ;             &                 d  ϙ             N               B                 X                                   L   .             r  O             \                                             @  t                             dL   P                                            DB                ^                                   ޙ             ,  T               ^[                             |     Qy                -                k             H8                 x             Tj                 j             z             
   y             P  ~  s                                          \               ,             d             X  \*               \q                                                                                            
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  n                             8               >~               n                               ڐ             "                 |                          z               j  G             0,  Z             $                    ֙             r                r             `  P   0                b             0                Z                x                  5             \.                              >             R	  }             H   x X         P       Q L L M J $N Q P M M DM tM N L hO O     M N N P O L N `N M  L  N pM xJ O M O L LN dP TL 0M N L      M  N  M O L P |N M O M N HN O M K DO P dL N  P N N tP N K dO O O M LO N N     <N M N O XK                   | X         P      d\ [ [ \ \ |Z |\ \] D\ \ \ [ l\ [ D] 0\     P\ ] \ |] \ \ \ t\ T] L\ X[ Z ] ] [ x[ \ T\ \ (] d] t[ \\ [     \ ] ] [ [ t] \ p\ [ [ \ ] p] 0[ h[ ] 8] ] |[ [ 8[ \ [ `\ ] $\ d[ ,] ( [ \ [     @\ \ [  ] 8\     {                 {                  m&             (&                &                5 
            8;o    &             &             &             2H   `&             ,  &               t&             8  &             j  &             6  {&             \V   &             0  &                z   &                &             D&               &               Bc&                &             F&             `  n&             B  &             X  &               i&               &             6  &               \&             `	  q&                  }&                &             >~&                 &             &                 &             T  &                &             X2  &             b    &               z&             &               `  &                $             6   a&               &               l&               N&               n&                 &             &               &             ~  &               p&             r  R&               P  &               &             &               &             L  V&               Z   &               f&                ~&             4  s&             H  &               &             &                   &               &                e&             .&             R  &               r&             (   &             F  +             v  \R+                               <+             >  *+             B  
+                 &+             
   vi+                \+             ~  ^+                #+             VL                   *               `  *             X  <V                   m+             \  M+                                H+             q+               s+               G+             T  =+               j~                1+               ,  +               "+               ^+             <  7 
                ;o    o+             x  y+             Z  *               u+             ++             N  +             \<  9+             U+             <  E+               *               K+             `    N+                +                  +                             +                &J                +             l                 *             J  #                r+             x  T   O                *             >  U                   a+               p;+               Ft+              +             N$  5+               0+                t   S+             b  *             Jj+ 
            X	                  ;             .  b4             B  0                  :                    N                H  @             J     A             @   F  1             &                D  L  5             *  v             B  n                                L               B                                   8  X                             h                 &                                                                                  >X                            z                               "                               
@               <   "	 
            &  ;o    R             \6&             V  L                                           T             <                `                     5               5             "  5             5               5               5             l,)               6             t  (   5                  6             66                  6                  6             f   5             8      6             V5             :  6             6             5             N  5                 6               5             	  5             2  5             5             @	  5             .  ~   5               5             V  5               L6             5             5             l5               P5             ^&6             Z:  6             D  5             5             8
  
6             *5             B  6                	6             5             >P  5               5             5               	  5               5             v5             `5             tn  5             J	  5             f  n5               @  5             @	  6             t  5             \5             *     5             V     6             T  5             85                   5             *   5             l  6                 6               6             v$  5             	  6               v5             P  5               5               |5               X   5 
            j          
S             @  G8             (7                  8                P                 8             Zz                -8             >  o                C8               08             h  I8             T                   7             4
  7             D  7             7             ?                L8                &    8             4                  7               "8               `                    8             ~\  7             b*F8             &F                38             D	                  7               >  68             r  $	  =8             p8             Z&  8             $     7               P.8             P  :8             <7             (	                     7               H7               %8             x  z  8               J   7             v  
8                7                58             V  '8               B8             	  88             7               b                7             Y                7                  8             ~g                8             &   K                8             "  8             "     7             F     8               )8                7             F   ,8             V7             7               jM                   7             V<8             J  7             t  7             7               8             h(  R                   7             $7             ,  l8                  7                               7             `!8             4	  #8             h  H   8             R<  7             r  N                8                ^7             l  tM             #O             (  <             <             =             t  =             :<               =             J  <             r  B<               <                  <             r    <                   <             ~      <             L  F<             B  8 =             |  !=                  =             "B<             b=                <               =               <               <             P  B  <                @   <               b   =               v  <              <             >   <             ~  <             D  <             2<             <             h  =                t  =               &  <             8  <             J     1 
              ;o    <             *  l  6                  =             <             b	=               <               <               =             F   <             0  <             (     <             
=             v     <             RF	  =                <             <             `  R=             n  .<                 =             
  <             *  =             0  =               "=             t=             h<                =             <                <                V  <                z<                  <                <                VZ             D   Z             v  rZ             ~
  Z             ,                GZ             V  >Z                Z             DP                   KZ             &  Z               :Z               hZ             b  Z             rZ               Z             lMZ               *Z               z  iZ             v    xZ               Z             J  I                   Z               8uZ                 Z             R   xDZ               T   Z             @  wZ             Vt  sZ                  JZ                                   eZ             X    _Z             ~Z             p                     Z               N  r 
            0  ;o    Z                L                   Z               Z             N  p  Z             (Z             \  "                Z               PZ             2  J                K                                     aZ             6                     Z             xZ             F  &o             o             no                  Wo             dt(o             l  co                o             2  @o             .    vo               2Io                  'o             &    fo             <  o             
     *o                 o               .o               {o             
  o             \`   o             \  Xo             x  zo             o                 o             z   Co             pYo             P_o               0o             "  Oo             b                wo             nno               o             DT>o                /o               xo             :  lo             h   `7o                 X                 %o               N  ~o                  \o               X|o             B o               >                   ko                o             d                 R               l             zP               7                          	  ,                             P	  B(             V    O 
              *      y               J                             p  N  x                tw             x             B  w             >
y               x                  0y             2
  x                 w             V  x               x               <  ]y             Taw             `  $             	   x             :X	  w             L  w             
  x               Oy             
  x             8   >x             	  w             B~w             fx  +             0   x             T   Zx             l0:             y             d.	  +x             p  w             Y	  x             H  x             L4                   6x             "-                0   x             N  px             &                x               2                                T  rx               b   x                 w               x               4w                Jx               :3             ^  y             w             Fn  x             r   :w             :   q                w             d    0                	   nw                -x             	  8                3x               x               (                Fx               y             J.                ;y                
w               /             	   x             H      	y               J	  x             Ry             x               Kx             0  5                x             o                  x             0  x             *	  *                   gx             l      x             >x                   w             @R  9                   Px             $  P 
            n  ;o    \y             	  7                x               
  x             4   x             
  Nx             
  y             D   '                 wx             >  1                y             H	  )                   x             h             f     c                G                x             R*                 :               t             J  t             D  >               4             .߶             p	  |                              2	               L
                	  ~             R  
  e             l`             Z                          h               r                  ֶ             6
  Ƕ                            	               F  Ͷ             d	  *   a             fɶ                  ö             v  u             p     ^             r             `  ϶             V  k                  ~             b  L                 Զ                               D             n             J  _             <˶             	  Ѷ                            	  `             ~               d   ݶ             m             :	  ն              &             8ض             4y                               @
                            `  v             2     ڶ             
  Ҷ             (  <                            @                            :	                  n  j             }               ]             b4	               	                 a 
            @  ;o                 D                l                                          \	               v  b             |   ui X         P         `  Й T H D l T H  @  (      $   $ Ě  @  ,     \  Ԙ   D t   L        H   \   8 t x x  h < ̜       ,  | Л    М           $  D  x	{                                  
                    Y               X             2  P             0                  g              !             x  ^|             L                   &D             c             "   z             
                   5             v  6               ;                             X8             2&  q               :             x   r             ^t               1             V                               "  m                                   2               D             	   	   e             4'             p  8             8  N                      J                                          J    /                0                    Q             l   H             !   =             J  q                o             ,"             Z   z             <^                  3             P                                  V             2v                             &                  :             L             v  @U             B                    &               4                                                 z               dj                                   }             2N  C                                [                             (    n                                 6             (  ]             	  {             "T4             x                 P  ,                                 k             0  
             ((                                p  l             ,  	                <             X  2                                  2T                                  	   Z             (  ?                { 
              ;o    E             <  *e 
            Z  f;o    p                             q             ^  ~p               L  p                p             ,p               p             
  p             $`  l                p               p                                  p             *  p             
	  p               	                    p             Tp             xq             Z                     p               4p                  q                                   p             8p                q             J   p             8  p                                  q                p               p             Y  p             4*  p             F   )               p             p               `p             t  p                             p                               9p                               {p               h  p             DX  p               p             2  p             T               	   	   p               p             ~	                  '   p                                  p                  p             tX  p             (             9   p             p             b	  n             R   |p               p             n  EP             0             V  0             NRS             $R             pS             z   R                  R             N  R               9S                  R             2  jR                .  	S                   R             @     R               (R               R             6R             |.  1S             
  J"S                   R             	  R             fR             bf  S               S                lR               RS             @  IP 
              6;o    R             z  S                  S             J  JS             $  S             ~'S             AS             
  D  R             L   R             LS               T'r               &                M   r             @  (Qr                   r             d    7r                ]r                                 q             (  )r             f  cr             
B                r               q                qr               b0                F  Ur               Dq               q             "                   r                                  &  #r                  Ir             
  Rr                >[                  r               Hr             z_                r             B   pr             
                  ?r                            q             r             D   Fr             ^
                 M   Lr               vr             h  $q             2                   K   &r             nf                     q             nXq             X
r 
            <  0         X         P   $ P  X   8 < x   h % p  T          l 0  L  d    4    @  H  @ 8      (     ( `   D  4   d    `   X  0 h D 0 t (        t        1                N1             :      1             `8Z1             \      ]1             ~1               1               ^1                 1             ^X1               1             D  1                   l1               h   1               y1               $k1               n1             d1               4`1                v+               j  `+                *             **             {+               :+             h  +               O+                                *               a                	+             ZR   P+             ,   6+                   +                  D                Z+             8t                e+             ><   [+             
                  +               Z/+             6+             F  $                k+             "  C+             @      *                 +             6  X             XiX               0  X               XX             v  tX             0      X               l	  WX             t  ^X             "  X             f  X                X             &  X               *  X             (  cX             z   X                 X               ]X             8(  pX             R  oX                  lX             6  X             
  Z~X             .      X             
  }X               L             RjL             j   XL             $     EL               *L                ~K               #L                n  L             r  ?L             .    K               H  L             (   :L               D   $L               "  K             ,  J0L             L             @  YL               K               AL             UL               K             K             K               Z             pTZ             2  \Z             *0   Z             
  CZ             <    gZ             hj   Z               Z                Z               Z                p  Z               OZ             )     Z                                 XZ                  cZ             r}Z                             ^Z             n                   Z             >   qZ             *  Z                  lZ             Z             z  tZ               2                yZ                                     |Z             Z             .  B!                   Z             1                   kZ             vZ               Z             x   d                   Z             <HZ             RNZ               S             <`R             :2S               :R             v  @  S                tR                N   S             j    R             t   X  R             (  S             ~ S                .  S               R             @     R                  R             >    S             jR               R             fR              R                  R             R             8      FS              S             ~  R             f	  R               hR             4R             @R               R             F	  R               R               \   R               R               R             ntR             (S             Z  .S             84S                6S             8  0S               0             n 0             :  (<P             B    0             ^(1             h0                GP              (  r0                  P             l  |0               N   0               0             6   P0               n=P             H2{0             8  0                B0             :     0             
    0               >P                  0             S     0             ^    0             .      0             D    0               0             v0                  p             pz   p             n               '   p               p                             +   p               N                  	   p             0p             p             Tv	  p             N  6  p             F>	                  +   p             p             <   p             p             &  p             <  p             4                         p                 p             V      p             \Z                   p             
  p             t  W                R  p             \
  p               n   p             b  p             r   .p 
            f   -	.	{             3|                7|             (  e|               ,|               {               |             V  R|             6  {             d|                a|               B|               :Y|                n|             T  {             
  ;|             v6|                z   {               :|               `|             B   p&|                r|             F  #o             xx  4                 M   o               Ro             B  uo             ~o             @   y             o                                o             xR  o               o             X  4o                <o                  Bo               s                 ^o             o                 o             4  o               >                qo             ?     ,o             P  ho             9o                  To             ~$e                `o               F   So               h  Fo             6                 :o             *  po             (   
              ;o    ;o             L   3o             vo             F   o             D  "jo             \,o             
  S                oo             V  |               ,   V             N              F~                                    ۑ             l   B  ~                	             "  ͑             h  ~                              ,   "F                d,             P                               8                *~                a                                    ґ             L  ב             N                  f               Ƒ               .             *               T  r               ؒ             X   
                -                (                `                  F  x[                                 /             ~                3                              	  O                                  j               8y             v  J             >  ~               4             R                |   z                                 -                "                 &   $~                ϑ               ϒ                Ñ             (   5             
                Z~               :  ]               v                  (                                              ͒             ˑ             F  ~                               u             $  K               R                <	                 h0             P   ؑ                 t~                                   (                ~                                   ɑ                +                            n               8   @             ,                \  ]             l                t~                          P                  /             ,B                (  &                -                                b  ~             :                  ײ                J             4   j               
             "                \  D             x                d                                &   w             8  d4             N                  J                 .               x             Q                          *                                  F  -             F                `  8                             j  \   (             6   O 
            >      ;o    $             *  v             dY               /             H  W                             4               `   
  ?                                                          H  b                                    b                                            X   n             b  $                VF                                     {                            ,   j               Z                                                                x6                 |&             .                                            V   H             F             j             P                                  .             P               6,             ,J                d                                                  >  `               "                R                 W                              ~X  	             (                |gr             @r             bJ                r                  } 
            hn;o    *r                   r             zh-r             zn  r             TKr             Q                  v  +r             X   Xr                                 "r                lr             X  9r                  r               R   r             mr             Z             T   |  6r             X                   :r                q             J  tXr               r             <                        q               d  q             P  5r               q             :      Or               =r               or             H    q               8  Wr             q               H  ;r             J  $r             r             D  
r               Yr             V$!r                               M   fr             l  %r             V             Z   `r               `q             ^2(r               0             ^0                  5P               0             `0             &  0                  y0             
  0             Lz   P               O             4P                6             lHP                0             .  *0               P               <               q             >0             R2n0                 KP               H  ;P               @0             b                 bJP             l  l0             ^  FP             r  q0             ~  0             X  b0                  0               O                0             |  :P             >  0             f   BP             T   vP             `0             4  0             *  0             `   h0             zDP             2  t0             z^  {P             `v}                              e}               ,                   }             Z  ,}             R~                }             H   q}               F  }                z}             :                 }             {}             j                 '   }             b}             $  }             p}               }                               1   }                  /             /   /   }               D   }             $    }             <  >  }             ^     f               (  f             h  0  	g                g             ,f             .g             t   f             (  t  0g               4g             <   0  f             
   f             $  f             j   ~             f               ~                   f                   ~                   f             "     f             `f             Vf             
  g             |   f             (g             
   ~                 3g                ~                g               g             x  9t 
            >  ;o    f             d"   ~                ~  f               F   f                 g             Qg             l  g             bPg               J~                "g             	  W=g             Hf             P      ~                tf             2   g             ^     f             j  f                g             *  g             *  j   ~               f                X  ~                f             4  g             \   ,g             0   f                |f                 ^  f                  f             P   f             *  Ng             B  g             r     eg             @  ^f                f             *   f             f               |g             d  *g             4   ~                  )g             ~                   f               f               $~                Kg                `g                 f             .                \               x	  )|                 |                 5|             `K|               f   {             x  C|               |             H
|                |             ^  l|               (|             `   |             b   |             f~  '|               ,|                Z?|               s|               H|             n|             
(  {             \  #|                 {               {             6  ^|             Nn   o|             4  |             B      =|             "   |             0X|               B  {             l  |             H  |             ~  h|             2D|             !|               $|             n  {             F  \|                   -|               J|             zr  +|                {             V   @|             R|             P    F|                  c|             (nL|             >	  |             &{             {               i|             %|               T|               }                j}             }             |   h  }             B     y}                               #   }             J  }               x}             4	  *                 }             ,                  }             J  p}             `  }             ,}               4}                }             (  }             .}             ~                  }             	                  /   |}             	                  <   }             $  
}}                }             }               }             d  4k}                  }             Jl}             n  }             }             l	  u}             r}                (                  '   }             |  }             V  }             $}             H}             *{               bf}             F   ~}               }             b}             X}               }                                #   }               (}               }                  }             	  }             Ti}                |}                   }             b}                 }             N     }                7W               VW             fv  W                                 \  V                ,  /             .                  hW             q     _W             N  5                   V             
  YW             &  +                   HW             hW             z  1                !   V               V             .  V             hV             p               z             0  d             h     f             Z             <                  d             rl                  v             P              q             p             ~               *Ç             m             ) 
              ;o    Y                               @  ݇                   ˇ             6|             *     z             l    χ             |   ^  n                :  g               P   Ӈ             "	  x             R| 
              ;o    ͇                p             J   `                                Ǉ                :                                                                   V   |               H؇             0               Z             >                 ԇ             B  
߇             b               y             J  0                              ]               e             Fpi             ,  }             V     \               &p             0c                            (	  w                v_               և               Ƈ             F     އ             ~  ч             $  ̇               P               ~	                            b               r             4	               T             ~  .             f                  ~             :  ^  ·                                Pf                Y                "                ~              V  m             6     
g                U              $I                 i                $   X             6	  ,   b              t<  $              &  h              H  Ug                  nf                f  l              ^   ZU              \\   Rg              4  ?                B                n   F  N                  i              &   bv                <   d                ,   O              N|  ]              ~k                6  g              j   dU                pJ              J   <c                  d 
             D;o    f              *                  g                 V                 m              h             $                 HU               	  ^"u                c             ,   yg              t   _                              b                   J              (  D              \   <[U                ^             1   Sj              "                   ,^g              J     e                              ~   W             6     {                              f                 a                x                   Og                ,   5                    g                i                1                f                j                f              0                  6  r                              v      jj                Bh                a              E                               `                Ξ                f              0                                  ^                 \                 E   S              &   Bc              Vg              j(                                      !                 l             J   R              D   q              @^              i              g                                $   D  %W             ,  W             J  W               Z8W             ,                 !   W             F   eW             X   |W             *  ~                V               V                V             lV                  `W             ,DV             Vr                -W             XgW             P                 W                !W             `  W             *     KW             B  V               2NW               r  W               H   ]W             h`'                   V             (     3W             ,  QW             4  :  V             (                 C   W                /W                   W             Z  *               W             bGW             >  xdW             AW               	W             f   RV             jCW             P  W                (V                              \W             *                  V             ^W             R   V             h                $  V             .b   V                ~W             N  V             ,    JW               T  UW                8V             HWW                  6W             h(  V             >(W             65W             <                  V             X    ,W                 >W                2             xW             bV             .  f             z*  Ug               ~                f               Ag             &   g             2  2~                 1   5f             	  f             0   %g             t  ~                 af             hF   o               T  w                 8                               N  [ 
            R   r       !             `j*                                H             V   ]                   4             	               v  ,             	  $               ݌             "               D               `             VX-               V                                 x&             Z             I             v               \               T                                       f               bN3               W             ^   z             0  Q             hތ                   	                               F                h               %               5                              v_              	               l  @׌             jx               D             T   .  Z                           H   
                 l  T                                  x܌               t                               2             ^@                x  <                            N             L،               X?                *               "  D                                     X             t               B	                               0  a             
                                $  r                               .A               o             F	  a                               !   }             (
  d                          +                  v             f  k                7             :  ,             n  p  6             .  j  v             B                                d  j                                     L                            P  $H               4                +   <             2                D                  0                               >   "                              |g             ^               <<                                   6              
"                L  0   $                           |                 '                                  F                             .                 Q               q             ^                                     x             Z                   V                                                               ,                  |             T  ,                :   N  ]             *     d             Z  d   z             F  
                                             r  0             R                                 .   %             m             $                   2                               .  b             .                                   &                 V                  R               0   \             p                                                6                                                 t             
   H               7                          D                               "                .  
            :  ;o                                                 8  &             D(             F  :               h                  FB   {               X             
@  f                            "     -                t4                             $  @@                  #             `             t   B]               i             0                             
p                "               Z    ^                            ~  6>               *             L   =               Bj             >  2$                               A             .  )                '   Q               6             $Da               b               ,J                                U             .  J   q             >    (                             8               6R             ,    %             &   ?               0  g                %                B             `  f$             '                   
                               /             h             z  |V             RL  6             Y                f               hT             t7             B  (  "                0;             *$`             n             -                1   x             2X.                 1   l             |                  R               6               2             &    5                  "             M   y              p                                             @(Z                <             >|                                x               8                   FE             f  T1             >u             D  V(             d4                 H                                           J                                               P   0                 Bc               <%k                j               D  k               L   c                           4  j             ^f  j                k             l  1q               j                ck               j                Tc                sb             Tj  k             ~  c             `   $  j             F   ~  
k               L    j                69c               j               pk             k             ~k             x  j               bYk             
   Sc               3k                 j             "   j               b             "   j                j             \  c             $  pc                   j                  'k             l     Qk             Fj             N   jWk             Gc               ,   j             8k             R   ^\k             2  Pc               ;k               Hc               k             &	  j             "   b  p             c                 j                	k             B   `k             k             >   p                 *  c             6j             6k             n  
c             $   |j               k                j             pd  Ck             n  k             0   nc             t   j                j             j             L   
   k             p  b             T    j             *   qk             0  ~|k                X         P   - . . .  . 0- `. - <. 8- . . ,;  - T. . @.     - 4- - - . - |- (- - . X. 8. , - - t- D- l- , d. P- X- . .     , ,.  - - - p. - , . . h. t. - , - . `- . . x- - T- . - - (. L- $. x. . <- .     - . , d- , @1 [             ^l             0  %                                           T  Dx               W             nN                                2  '             D  k             &               `             b                             8x  X                                x	  :               N  J             6   >t             n                                              dB               ]             b  Y               `               2               o             P  8                            ,  {                  :             4  n               L                          ndz               q             v             p  =             (  T                  #             
  R                                                             LZ   e             \X/               2                              f   &             V|                                0                D             >   U             D             8  !             &  9              4             2  ~             I             <   S             n  $  M                                >  "             
                  )             l`   
              ;o    j             d               J               &^   ͗                            
	  ԧ                            6>                R                 r֧                          6  8               	                  #                ϧ             f               @  ʧ             0X
             H                \	               l                             |t	                                 ˧                          6ŧ                                         ҧ                               "                     n             
                  Q                x               h   ^             <  
                 Q                h               #                   `               4ۧ                                F                   ܧ                  ӧ             x             $                -                ɧ                                               &                L  ͧ                               .§             f~               L     է                                -                                  4                                T  Ƨ                 3                                 \	  @             ^f!                             t             B                X                                *               l               h             &  R   ̧                                             Vh               U                                 ħ                                                                R                                                                 L                                                                     ߧ             ,	                     |	             >4&	               8  	             2                            f  B9	             J  	             _	               *  	               F
                            H(	             b  T
                 	             "  Z                              6  d               b)	             >df             b                              d                6                 :E	             JL             .  	                              	             N  p             t4               :                 lP	             .  j	                                         ^  $	             c	                |                             l               	  -	             d	                x   o             L  V	             ,               f  	             
               &               \               "  t                @                 x                d	             Tl                 	             @b   H	             &I	                   $	               D                                              |$  x	             ,  u             $   	                          l  	             8   "3	             0                F               >             B             >      4	             2     	                >	             >  J  t             v             (                               ڲ                               ٲ             ܲ             	                               ,˲             r  z             _               Hl             v                E                
                   
             @f               m             f  H  ղ                                '                Ȳ             V               >U                   ²                                  β                            *	  R    
               ;o    ݲ             L  d                pvӲ             x  `               8Z                          \ǲ             ,  #                             0               2                ^	                   !   g             X.                6               
  v               tŲ             D	                  ~             R               ~ 	                   E                                             	               h  Բ             2  d]             $                  s             <                  !   c             L
  p             .	                                 ,  >  ֲ                                           P     ò             2	  в             ^
  ̲             v\             zV               V                     b             p                                      ʲ                            L             f   q             F             
   H                   Y             
               \n             (	  ^             	  u                  y             ^>	  X             d   &h                             p                                           4  
   "             "D  6               E             	  $                f               Z             O             D  F
  i               s             ^@  7                            c             <  0             	  	               ]               N             ;               V             P  %             X                (	               @  (M                            |	  +             Pl             N  b                                t8t             P    G             V_                          :
                  bj               T             ,  ?             4'             v  o             Njd             H  l                   *                          d	  /               z             0                              
  t,               F=             	  W             X                   >   k                            B                 b               L                   !               "                 Q             6               D             (               <      r             <  &             t   :             B  1                            0P               2             j               %                          n  `  6             &                  >               n                                  D               `                                   <	               	                              z               "
  j                                       rH             :   63                                             p             h                                                    D  8             8               \             `   4             D   ?               e 
              ;o                                                  T                  /                                            Z             *  )             B  -             4f                                .             H,             R                            
                  j                            F                                               |B                  F                                                            B   
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  B                                J             d  `                                                   	  0                               h               F                  p               H 
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               P	  $               }             4	               <  |             	  k             H                                n  ,t             (                               `             Zr                ns                          Bx                   \             &L             d                               L	               P  T               8                     S             2                       K             F	  2             p               X               
                  \             Z               R  n                                  \               h                                           V\                                X                            J                   t	  D             Z   `               *                             >                                   P                	               ::               6                               J                                 J               @             b               @               6	                                  x             R                                   <                                                                  f^             4	                 lV               f  R                ^                 5                B	               V                  z                             |             *             r                5                                                     $                                  V	               	                            &                                                         NR
               j                              $                                   R             Nf                               h               ~             n                                 4               	               |               n                                             J	  F                                           4               @   f                    ߾                               |                ~             z             @               v             *X   ޾             ~  j                          p             B   Ѿ             @.             PV               w             :               :"  v               Lپ             D  R  ;               m             `  k             Ll   þ               8             *             0               L                |               X                  l8  Ծ             *                                ľ               ھ                p                                |               N               tJ             <Z               R  
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  X             &  PY X         P   Ȅ	Ľ p `   d  $    @  4        \ l H     м    < | \      0   x           X ܼ ̼       (    P L    ؽ  ܽ p D  d          Խ ` t  | 8	0 X         P          x   ,  |             4  0   8 ( p     D         ,           `     L  h    P d t               ( H     p    l ؑ	5             8             b  8             :      9P 
            dd                     	  4                             Bd  ~~                             ^*	                  t               &"K             J             @  K             r  H                J                x   J             t  K               4J             $rx                   J             :V   J             v                    J             BJ               K             >4
  J             J             K                 K             F  hK                                  J             HD  K               J                J                J             B                     K             d  "(                J                   6                J             K             8H   
                 ;o    K               J                  <                J                               J                  J             K             n  K               JJ               ^J                :               K                                  K               J             t  J                 J               d   J               J               J             z@  8                K             f=                   K             v  J               x7                   J               6K             t                   J             <ZJ               @                  J                                  J             ^T   J               ZJ             X\  K             K             8  J               6J             T  ` X         P   m 4g g f g ,g th g h \g f df Dh f g f pg     Hh 0h Dg g xf g f h g ,h g |f xh @h g `f g f f  h ph g f g     Hg f (g lg g te (h $h hg f g g f h f h \h h f f f 0g g Th hh h Lh Ph g g g g     g f @g \f g dq L             t<               <             <             tL<             Z  <             <             ^<             2p             p               V_               P  I               |             H                F1             R  ^   q~                                                               %               h~                                n   G                ~                [             ,  J  =               M             V   .             .>             l     Z 
                  ;o                 p             J  H  e~                               T             b                  F   g~                                *                0  h             Bd~                             	  l~                                    L               d             D                8                N  .   x~                                             L                  \             B"             N                (@               >  q             0                   :             $i             N  ~                                          >   i~                               D   X  Q               H                          :J   7             |T  o~                                  Y                 x  #             :               
  4                               6                                                          f)                  *             8  @             :  b             ^  6                               r+             \  t~                                              1             `  j1             "	  1               1             x1               z1             T`a1             :   1             b$	  I               1             r  i1               R1             6   1               1               Y1               Z	  1               1               .  1             `  1             l1             :  1             j   vs1               1             
  d1                  t1             F  1               1             
  e1                1               R1             o1             1             p1             $  1                 1              >  r1                  1               "  _1             1               1             1             V  g1             z1               ,1             f  1               1             ~  1             \	  1             2	  :1             L   1               1             |1             4      1             8  1             1             
6  1                6             \  P                  O               &                    O             d                   O             F   *P             `O               ^
P               \             O                                O                r                  O               P             H-P             j  ^  O             jO                                P             \  TP               jO                  i                P             R  !P             H  n                  O               4O               O             L     ,P               O             n"O             
  O             L3                    3P             N  O               O               1P             2                       P             |O               J   O                  O             XO             L  JO             .      O             |O             R  /P             6  r  P             8O             `:"P                   O             V~}                P               O                                  P             n  O             bO             *                  O             jDO             N@O                 P             |  E                   O                tO             :     O 
            B  |		             ~  <                              pJ             J                             J             h  TJ               |J                                      J               J             L  tJ               J                 J             $4  J             8                       J             h  J                J                 XC                J             b                          j   4             6@  g             z  E             >o             :               P  $   n             6               6   l             $                                F                2  @  r             @  ~             <             T                d             B  >                   &                                 Y                C             "     $             <               b*                J  $             :               H  G             2                "                .  u             j                    t                              1             >L   N                              P  `             (                v   =             ,                     Re               L              
                              6                R                            R`-             ,  ,  H                          ,    +             r                 
             X   ?               '             W             j   |?                  S               ^]             ~&D             ,                	               N  b                F   B                 .;             h             B~  o             (t             <                k             C                =                m             :  2                            L                   J               X                   z                              Y             N9                                             x  @                H                             "               P             :                     |  U             ,0                                                8
  4                                           f                 Z               d               q                                  r               w             .   Jc             h  7             T                                 \   ,                 0                             >  5                                   i                                   L                             <  l             vB             4                                                 R&                   n             R   d                  PO                 P             O             O             Nj                O                                      0                "  	                 O             (^	  P             P  P               O                  O               b'                   O             2P               P             	  #P             &  O             f   |O             R.                O             dP             p  ML                VL             ,    XL               X[L               n  "L                K             L                  K             4L             
L             K             bX-L             f  DL             L             OL             T  \L               K             
  L             >QL               K             (  bK             dp   'L               K             
  K             f  ,L                  K             <      K             L             Nn%L             "   2L             V    K                  .L             K             f    +L               eL             N  K                  BL               K               WL                H/L             8  3L             D   ~;L             B  JL                 K             r  JFL               <	L             n7L             ~
  PL             6   K             f  K 
            :          =L                L             '      L 
                      i             >ǀ             Bh             j  _             
  m             b  K                _K             	  vK             tbO             ^   FO               N                 G             ,  X                8                     O               zN              LN             	  O             v   JV                N                   N             
  N             R  N               N             :      N             6XO             >    [                  N             hN             <  N             6M             0
  N                O             n(  N             	  #N               N             R   Z                =   9O             v
  x N               Z  3N               `N             J8  O                yN              	  N             HT             =   N             f  |U                C             p   AN                6O             XY                 )   N               v  N               R`O               XN             (  O             ^      N               N             J  j                  N             h  B             	  N             V@O             N             N   ~N             I	  N               O                                   N             \N             
  N               2M                    >             N             >H	  O             (R             
     kN             L  O             TCO             `  M             Z  :L                 	   C             `  N               \	  N               
  ;O             	  G                N             I                   M               n   nN             Vf  LO             v  ]                E   N              V
  Q                N             6  ?N             V  >N               N             n  -O             N                e             	  Se                *  e               e             0Rqe 
            	                       @               r                `   k~                /             V  l                  Ps             D
               4  ,r               w                               X                 @                            2j                                   V             .V             ^             O                F               r                  D                            N	  x                                           n                 9               A             ~             zp/             1             "                a             >2             j  =               H               {             >                                 8h   [             0  y               T   e             2Z                 _               2             j  N             T                   :  T                                J             J                                  `  ]             J	  l                              >  B                            J	  N             t               x               j                 L             F  ~               S             <p  :               T  Q             x             \   Y             
   PM               X                 n                               ;               TU             @                                                L               <6  b             P  bb             ^ob             z$  j             T      j             2     ~                   j               ~             "   ij             >j             H   
                B_             B   A                                               &             DF               ?             B    @             $                &C                 ^             L                  @                 T             :   &             b    I               $J                  K               K             $   `               n               	    (             ^E               7                `  A                  .             *<	               :  &             \  8               S                	                T  %             z/             	                               ^;                 D                                j               O	     V             	               (   6             ^  >B                )             ;                              0F             >                W                            `  -             ^   f             ~6             
                                  O                [               b  <             z  P                                J                !                   v                 =               &	             RVM             :                  %                R  C                '             R  "             Z                   E             !   3                            $B                N                >             .             r                "  .               :               j                               d<                +             z	                    5             F=                                               z  Zo             	    *p               2p             z  o             <  V  Bp             Dp             d
  Mp             n  o             4             (   )             0                l  
               N             ,                |               "T	                                              B                              h               V  q                            6                                   D               >  x 
               X  ;o                 f                                               
               V                             "  s             p  Zz             rH	               8               "               d                              
               ^                ^                   V               v
  ~               X                            <               D             FF               P   v                                                         @                 {              t               @               	  *             :h                              
  v             $                 	  .|             X                                 6                                          0t                <             x                                 H               6	                 j	                              r	               >                          @             l                                  n               (             N&  Cz             $y             
  x               ~  @y             ^x             	  8y             D	  y                  `x               ,y             _y                  *y             pn   x             %z                y               y                 6y               "z               x               {y             Cy             :  y             ^	     yy                y             
  Iy             ^wy             x               *   y             	  & 
            ;o    x             
  :5x             zy               n   x             @	  d  ry             
  [y               y             >
  x             y               x             ^3y               y             Dy                2z               ay             z             xax             
  y             p	  oy             
  :y                y             2   F  cy             (x               Zy               y             	  y             :Jix             t~  x             x   tx             J   Ly               
  y                  x                zx               *}y             L$  y             	  hx              z               bx             T0z             y                   dy             j	  y               ky             	     y               >y             (   Dx             	  H9y             
  ,   y             	  q	    n  `  (s   T Tp Lp     ̾ \, l>  4k M l  h r ` : t  E hJ P1  ~ (  D P <r     dW  Դ 0 ` Ĳ  ]  < ( ` -  y L x \	  ` > ? <Y k X\ c ~ h     O  0I d
  c ̯  P7  i 8 - s    x     l m     n 0 h \n  8 t   xy ( z   $  p ;  _ L7 PZ D6 [ ,   l ؤ  D    	 : 6	   0R	 x	 |  	 Я	 @	 T	 M	 	  	 	 
 	 (}	 { d p
  l k	 y
 
 
 ,
 `
 
 p t
  < \
 h Z 6 d
 | d
  Л T  H T $ Ķ  hA  LX V
 b   X p     \ ,   R  hg  Hh 
  < Lr  e  ^  8  X  $ B L~ @ i   t   L1 G XG  \h | h  |z  E  >   8.  x< B @ xh P
  L
 p}  D  P  d T  (t tD $ {  y p о      ,# < d   T Q  	  ܨ  H , > [ L ,i 8	 xd  S  0   K P	 K p> \> z T  ( \6 d l |    & P 8  a ȃ  @e  le C \C T T x L  S ' @_ ؍ \ &  !  8 HM  2     m Lw \ H ] ̪ H p_ @ H" <9  0 \ \ `Y `   ̰ 3 |     ` "  ԥ     D   01	p7	 
                             <                  (7	8	P	˸C   j  p7	7	h 
           7	8	#6	lN	                          <        d L         7	88	%
                             <        4  ]~                                                             V     y             t             	  x               k                (                Jj             6   N  !                0                \                      Z             
               <jS               r               Z]                            	               t                 6  u             	                     C             @   i                                            V  D             ^               f             
  F             
               T
  7                             )   V                                                      p  T             f                    %                	   n             	               	                 :"                   `               v             |               >               o             ~                    ;               N                                             $D  x             s              	  1                                           
  r               d                  #                                fS  k                   H             l	               $     d              k                 ,                               M             B	  2             
  c                          	  6   A             N                0                                    H* 
              ;o    <                                         7                V                     6             
  @             ^W             	  m             X                             0D9             r8             0                  4               (                             :
  l             d	  Z  ?             	  =                 vz             j	    %                 &             
  %             	  6&               X%             $8&             
  	&             d
&               %               p&               8  $&             T   %             J  %               <&             Z	  %             6  &                %             h  ~%             x%             :  %             %             F  %             &             :  ;&             %             rT	  %             J   &             %               ^%             t   %             q	  &             -&               	  %               %             v  %              j%               %             	  &                  0&             tj  %             
  &             2&                  %                *+&               l  &             %                 &               %                   &             j      &               &             T  &             <	  &             
  T%             `   &               %             
  %             P  %               %             D  4&               B%               
  %             0N  %             @  .  ,&             V   %             

  %                P&             4  5&             2
  %             :%              p	  %&             .'&             @&             j  2&             B      !&             8L  )               N  )             C*             0d*                *               0*             V)                 _*                                 -*               R`*               f*                   /*               )             >  *                          )                  Y*             n	  )               )               X*                               X  I*             6  $*               0H                )             V
  *               6*                              -   )               ]*             `$  T*             J`   )             `               (   9*               j                   [*               *                2 
            ;o    *             *               E*             8  &*             0=*               *             :*             a*             ^   )             ?*             )             &  7*             6b  
*               R*             	  *)                               *             z                *             x                  )                3*                                (*               )                *             hF  ~                U*             D   d                )             B  "                   )             (  )             x	   *             P  **             "  <*             B   )*               e*             	               
   S*             v  L)                                  ,*                 V*                 M%             	                 )                vQ*                                 )             d	  B*                   *             lf  )             BX:*                +*             z                   \*             D    ,                 ,               ,             j  ,             Vn  ,               
-             	  ,             &,             >  -                $,             	  ,             J  -               ,             Ll,             p	   ,                ,             F  ,               ,               -             *  ,             4n   ,                ,             F0  ,             z,                ,               -             @      ,                 ,             H,             >   d,               d,               N  ,               ,             r  ,             |   ,                ,             |	  -             0  ,               ,               ,             ,               ,               *  -                ,               r   ,             p  ,               ,             z  R,                ,             \   ,             .  ,             :n  ,             ,             ,                 ,             2H,                ,               ,             ,             ,                   \(             z,             	  :,                  -             ~
  ,             D  ,               ,                   ,             ,                  ,               ,             n  ,               B,                ,             |8  ,             <,             :    ,             @  2             (  
	  t2             T  D2             z  2             	  b2             $  2                ro2             2               2               2               }2               p  z2                J2               P2                 2                `2                   2             B  2             h  2               ]2             `R  2               Z2                2               Z   V2               2             2               	  u2               2               Y2               n2               42                2             _2             N2             X2               T  2             &2                  2             4  2             n   2             ,	  2             ,  2               K2                    J2             	  2             "   d2             ~2             &j2             $	  8S2               nq2               ^2             <  2             P<R2               2                g2             BT2             |r  rB 
            ^;o    2             |.  2             Z  e2             	  x2             
  h2             
l   N2             2                `2                 2                 2             @T  2                2             "  2             2             Pk2               2             Z	  2             h  >2             2b   2             N  Q2             ~  E             	     D             FD             4                  7   D             D             ~             (  D             Jf~             D             j  (  D             F"	  D             @~                D                nD             D             x  D                 E1               ~             D             t  D             tD             (4  ~             :   D             &  D             Vf~                   
E             
R  D             J  ~                D             H~                D             n  ~                D             VZ  E             F      D               fD                D             b@  ~                D             ~     E             8	  D             HD               ~                 D             BnD             D  D             	  6  D             F   D             	  hD             ~   :D               ~                D             $  D             B      E             $   ~                D             	  D             ^D             h^	  D             4(D               Z   ~                 D               D             f  D             j   ^E               $  D             h	  ~                   D             pD             :Z~                 D             	    z 
            d  V  ;o    D             	  &  D             >JD             V~                   D               D                 D             XD             P  ~                D                vD                  D                6D             V  E                  ~                D               ,                D               jD             $  zD                  D             .     ~                   D                 D             j  D                D                  B             t  M             	  M             H      B               B               aN               B                $B             h	  @N             B             
  B               *N               (B             X  N             Z	  B             d  B             4
  B             	  N             [N               ,  3                   N             B
  N             ,cN             ^B             l      G             	  G             x  8B                B               t   N             >  ~C             `x  (B             `N               0             d  B               B               	  B             x  B             h  mN             l  N             nM             
  B             $	  C             d4             n	  B                 -B             H  M             |B             J   ;4               ,M             ,x              f              
  B             RV             `  M             .  |             
  4               B             ^   ~M             2  $  S4             'N             B             	  j  N             zM               M             ^  *B             td  B                N             8   M4               4             $  B             T  B             
	    B             FN               6G                              .B             	  8v             	  J               v؀             ^T             k             B                                     2              N             ^@                              \                 i                               !                ^:B             l]B               iB             r  zB             
$CB               B             J
,B             "  r   FB             B             VB                nB             ~~                (B             DE~                   B             

  ~                ,   uB             R	  <B             Z   B             "	  1B                 ?B             :~                B             P  [B               B               !B             H
  xB             &
  \B             	  B               B                ;B               B             l*B             
  
   ~             ,   B                $'B               ~                   NB             h>  B                 B                  ~                   &B             
  r~                B                RkB             "	  	  ~                A             
,  ~                6B             BB             z  ~                $B             
  B             |	    ~B                B             <
  JB             .     -B             L~                   @B             "  B             	  #B             	  ~             &   D  IB             zEB             2      =B             f~                _B             r	  B               B                ~                {B               /B             WB             OB             <  "   ~                   pB               LMB             XB             	  bB             r  B             2     ~                   ^B             t*  K 
            l;o    LB             X  ~             	   B                 fB               lB                   ~                   B             `     ~                  sB             D	  |B             ,
  ~                YB             ,wB             P
  F   !             V   d             R               |ˁ                            V               Fg               ̀             	                                  Jj               B             0             	    ݀                               >                4+             d                               H                                   4               J  A             D>	  Ѐ               Lـ             @  #             ,	  :               B               n-             Hb             NV	  2             .  \             @             	                    L                F                  L                                >             6                 |               p                                   x             	  TM                               (                   L  T             ^ˀ             b               T  ,I             *P                                ~             4  pJ               AK             F  ;K             >   :IK               J             hp  <K             \  <	   K             "  aK               ~             '   6K                   K             :  RK             B,	  ~                J             j 
              ;o    J               K             <~             -   K             
  0~                   1K             @  CK             vlK                  ,K             4~                 
K                 FK             	  K               ~             ;   bK               :	  ~                   PK               OK               ~                ;   J               j  MK             h	  ~             0     K             l  K             ~p?K             4h   eK             r  (J                =K             cK               6  VK               J             B|~                K                }                J             b	  ~                K             p  J             *  ~                J               ~                K             ^   *K             ~                 2K             B  ~             :   -K             R   K                 `K                 .K               zUK                RJ             B  K             &  7K             J                   >K             P  J                ~                r  TK                               J             J             T	  tK             	  * K             	  J               v   YK             J  J             ,  ~             *   J               ~                J             ~(~                   J             0  $K               ~             "   (K             *   'K             ~                  J               LK             X  db             =b                  Bb             Wb             &  mb                b                `b               b                 tb             >,	  \b             N  nb               b             f  b             *  z  b             H  {b             @Z   :b                Hb                _b               Pb             *9b               ,  |b                   Nb               b                 b               fb             
      b             6  zb             B  b             vb               L	  xb              	  b             R   b             0  b             b               Fb             N  b             
  b             f  ~b               x;b             	  b             h	  vub             	  ~Gb             *  (  b             t$wb               Ib             <  jb             b             6[b             F   6rb             `  Hb              hb             &  7b             t^?b             	  b             &  b             \  V	  b             b  Kb               Sb             ^Rb                  ]b               b               b             
  qb             \	  b               bb             zB  H               >b             Z  Jb                b               Ub             d   b             h	  b             :   kb             j             ^	  p  j               f  ~               j                Z  j~             8   j               j                  kj             :  fj             T	  ~j             H~                j             4
    ba             b  j             @  j             Z  j             j                bj               j               j             bRoj             0j             R  (_j             \mj             j.  j              Pj             j	  j             >pj             	  j                 j             z   <j             .bj             
  j             t  	  j             *
  wj               n  j                  j               j             z  "j             .	  j             j  uj             ~                j             @lj             b~                j                "j             ~                aj             P~                 yj             <  D   j             f  <|j                j                ~                   j             *     j               j             F	  p  j             x    j             (  ~                	   hj             j             J(~                   j               j             8  ~                8   j             J  j             *	  vj                ~                j             :Z~                j                  j             J  ~             /   j             d   T~                   j             	  j               ~                {j               j             @j             RX  j             p  ~             	   j             	     j             <  <o             
  Cp             *   l  Np             	  Vo               o             (    =p                  Kp             8Qp             o             d  Pp             .p             f.   o             B  h   +p             |	  o                -p               o               p             Fn
  o               p             >  o             t8  o             lp             4Hp             	p             Vp               o               o                p             X
  lo             0
  p             (  8,p             r
    &p                 	  o             	  <p             0  $   p             &     0p             R  *   #p             b  p             Z	  H	  o             "6p               @p             \8o             `	  o             t   o             Rp             :  o               o             .  p             Zo             p             
  `o                o               V3p             p             
     4p             o             	  W8p             :p             L     o             R   p                 p             o             > o             "	  o             
  JGp               o             0J
  p             @   fi             ci             
  4i             d"oi             6	  i             (  hi             |   Wi               %i                X   ^i             Xh  i             
~Zi             zh             t  >i             l	  _i             ph             R
  Ki             6  i             i                  i                H 
            4   ;o    3i             $
    i             h	  bh               Ji             	     Ri             tzmi             V  1i             ,j  i             	  i                N  'i             ~  gi                   i              Qi                   [i             $	  =i             0^Ii                  i                .2i             V     i             L  ph             |  Ti             h
  !i             ^i               Gi             Zt.i             ni               	  i             *
  i             	  H  	i             i             h             B  N*                L	  Fi             i             |     <i             	  h             p   2i             H"i             T  p   Oi               i             h             (Ni             T   h               i             
  K             V	  ii             6     Ai             0  Ei                	  -i             8   >  Ui             B
  \	  h             t  ?i             
  D               h             $  &t                  Zt             Dt               t             $   ^t                $~                <t               (	  [t             z$r~             *   t               6  ~                Ut               ~                   It             Z	    Ot             
  ~                 6t             (    =t             @ t             Z  et             "    t                t             X  %t                &  ct             4$;t             X8  it                z  z~             *      "t             T
  
  ^t             J      t                  ~                ft               t~                4o             *Mt             D	  
t             	  ]t             4t             2  s               Jt             l	  s             b   y~                   _t             JKt             X  s                :t               s                 ~                   s             T*s             
bt             *  |~             ht               ~                  s               ~                t             r	    ~                   jt             }~                Qt             L  Yt                D  s             	  t               t             ~                Nt             (
w~                 >t             "   #t                -t             ~                   s             ~H
  Wt                t             	     s             0u~                1t             r    s             J  s~                 't               
v~                /t             h  Xt               (St               {~                   t               ~                l  gt             x    t             P  >*t             	  s             t             &~                  s             >t             4	  e             >}e             ,	  e                  e             e             r  	  e             L	  `e             ye                `  e             8  ^_e             pde                   ke                Hpe             e             X$
  e             
  xe             	     Xe             D   8  e             e             e                   ze             &
  e             X   
            ,  ;o    e                e             
  e             J   r  he             j
  e             xv|e               e             L      e             D  "e             e             N	  e             h   .e                	  e             h   e             bve             d  e                  e                D	  e             F   e             e             B	  vse             F  e             e             pe               6e                Pe             De             Z	  e             Pfe               e                e             Pe             te             	  &  `e             N  ^   e             t
  "^e               re             F  
  Te             L
  >	  e             N  e               e             
  ie               e             $n  e               &e               	  e             <
    Ue             F>e               ~e             o             v_             <7                   F             .  Xt                "w                   D               x             &	                  z  p             ,4w               y                :              
     G                j	  u             v                              n2~             ^	  N                [             j  b                              hd                            	               @             F	  I             z              @                   l             6zR)             
   
                n  X\~                                rp~                                ~$                               F                
  $l             (   Y             l                Q                            Vf             ,j               ~
  g                      u         {  {  % t                                         i             8H
  Ā                  &~                m             x	  &V               `             @    a~                          dP             pE             $
  4               d  &
  B                                         l   ,             ^  c               |             p
  l	  `~                             
  b~                             P               H   ^             N                 bR
  S                f  M             p  j   f~                                  
                   >             ^
                 :   \  Ix             
   {             X                	  _~                k             ng                              >f             J      9             xK             Z7                                Xv                !   ђ                               '                    ؒ                   Ԓ             !                4                                                                 b                          H	               B                               @               <x                  x             ˒             >  p               	                 J             d  D                :               Fj	               P                                 ^ɒ                                4             8	  Β             p               *  Ȓ                                ~  |                                                   ͒                                                                                   (
                               6   ǒ             r               ,               l                                                                     f             |	  ܒ                                 m	               V  }             R  nВ             :j                              8\                  Ē             &v                                   ֒                H               t                             >	               Z     ߒ                                               \  :  y             ,*                                    ݒ             	                               F  z                                               `                                               '                                ~                                   ے                            p               $                 ~                                                                                                   Ӓ             $  v               &̒             ,               P                      Ւ                                                d:ƒ             T$             \  ʒ               	                                  6               
  fڒ                                (4ϒ             J  Ғ                            Xl	  Œ             2
  ג                ?             9             D      U             d             w                 R               j                            j               u                  ~             /             b   f\               B                :             J                  =             .   l<             ,   H                                (5               0             L  v             <T  i                              &                .                 tK               H]                          2  8             :  G                            4b               r7             r"             &	               P                               T  r             Va             z   Nq             V  $`             Q             h  \                 1             *  y             "   h  :             e             &D	               ~  B  @               6               
             n                R  H  s             0  x                          PF             	     }                            t               H  3             x(                   f  |                 p             >  ^  U             <	  n                   S               @   m                          ro             N             n4                          L   
   g             6  '               ,               _             ^dc             2   kk             v  t                                              2                                  F  b                               T             	                                                   z                                <                               &                  r]                                          X	  \               B                H             :             l                          r  f               f                 V                               9                                                    "               +                2	                  v                   1                    P               ,   `                              r               z               B               b                1                             F               t  t                                                                <J                                              J  a 
            4  ;o    	             f  @                              j             8&                                  ZR             d  
             *               *   )                               t                             Z             #                \  *                 9                V   t             "               D                                                        @               x                 R                                (                                                                               `"                             (R	  !                @               R                          h               a                             |t                 q               r             N	  T             |D  }                             FF             RP             $z                                              b	  t                   s                                                          6                  n             x                F  J               \   S             d  p  l             v^               B   \                k                                         L   pC                 @             h.             d   K             |<             T               {               `  Z                d[                          R               b8             H  c             J                 \i             X               l  t               8b             N7             b	               b               6   D  d             Vne             	                    G                2O               z                4               v  *W               V             V                  F                 2N                N                               I                          v  o             >  =                            .                 h             *$  |             L    6               E                            J*             L               f                p               v             (     %             N               N	  L  
               J  ;o                 &	               6               R                \               	  *                   A                v               r                                    {             ,                                                            #   #                             d                X             ~  (             H
                 0                          p	                                                  	                    	             	  F8                                         ^
  
                             
  X4             	  X               l               x   #               <&             4   1             te                J               J4               $                H                                   j               f               D               F                                            	  |             >  .             &              (x	                 t
                            p                                                  |                #                                 *             D                  3                               r
  
             ~                A                V             	                  #                               $                             
               j                                              	  @                	                
                            f               "	                    5                          %   %                                
  /             r                )   B             t(                               
  b               u                r                            b             x                Q             f                     v                                |(               $P  p             ~                P   ~             :
  g             .*	  _               R9                            ,l               t  E               p             Z   +                e             h  C               p   t                W             	  4             l   fm             xM                F               ^             0  ;               \             @   '             z  Z             "^                0             >6t               J             4d
               0  Y             B   G             .               d	               F  q                            H4               68             Z
  z                f  h             l      O              LN             	  D`             B  i               $	  :             l               ty                                                                          Z  &L             r                                 l
  2}             !                ]             T  5                 s             )                 3               H~                !   vc             TP             p2  ?                ,             $Dw             )   -               $             	  |             +	  I             >               8                   h  z                n             |y                g             @                    `               nn~                l               `               D   Ja               `               0  X             p  Sa             TZa             T  t   b               >  Y               'a                 `               a             	  a                B  a                 `             R  X                xX               R"a             Ha             X             a               a             ;a                `               FX             ^  `             `             ha             B  X               .a               `a             /	     a             P	  a             *   V   Y               `             J  Y             D4   `               `             n`             a             &  sa                `             da             d  X                  )Y             Ta             `   da                r  `             .  `             `0`             `               z`                 `                 a             Ea               ^`             :      5a             X               X             \  `             `j  `             Z  n  a             B  %a             L      `                a             2  Bb               a             T  `             `Ia             Y                  Qa             r   Fla             D  X             <  a             Da                (a             n	  v   
                      oB             V  ,	               	             , 	             *	               	             *
  J	             ^p	               <g	                d	               	               J  	             BHd	             RB	                	             6  -	             .	               h             0n  E	              H  k	               60	                                B  R	  r	               (	                  ,	             v   4  f	              	             x	             RF	             d=	               N	  _	                   \	                  	                	               ^

                r               ls	             <	             	    6	             x	  \  5	             l  th	               $	             TT	  /	             l                 U	             A	             C	                   	             B     3	             &             	               	  $               &V	             R	               $S	               P9	             >DN	             r   D             hL                    i	             \     #	             0	    	             r  '	             B	                  	               0
  p             \  8	             P	  ;	                dO	             N   o	               \L	             
  Y	             Z6W	               Z                   J   		             x
  1	             j	             pF	               l          DONE!!!    C                                                       $                      
         valentine.s       k         	                        